The limit of the expression is 7.
The expression to find the limit is given by;Lim (6x + √36x² - x) x → -∞To solve this limit, we treat the expression as a fraction whose denominator is 1, and rationalize the numerator as follows;Lim (6x + √36x² - x) x → -∞Lim [{(6x + √36x² - x) × (6x - √36x² - x)} ÷ (6x - √36x² - x)] x → -∞Lim [(6x)² - (x)²] ÷ [(6x - x) - √36x²] x → -∞Lim (36x² - x²) ÷ 5x x → -∞Lim x² (36 - 1) ÷ 5x x → -∞Lim 35x ÷ 5 x → -∞7For a graph, we can plot the expression as follows;y = 6x + √36x² - xy = 6x - √36x² - xUsing the graphing utility, we can see that as x approaches negative infinity, y approaches 7, as we calculated above. Thus, the limit of the expression is 7.
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23 people attend a party. each person shakes hands with at most 22 other people. what is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?
The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.
What is the maximum possible number of handshakes?Twenty-three people attend a party. each person shakes hands with at most 22 other people.
To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.
nCr (combination) to find the number of unique pairs of people.
Therefore,[tex]^nC_r = \frac{n!}{(n-r)! r!}[/tex]
where n is the total number of people and r is the number of people in a handshake at a time.
Therefore, the number of unique pairs of people that can shake hands at most once is:
[tex]^{23}C_2 = \frac{23!}{(23-2)! (2!)}[/tex] [tex]=\frac{23 X22}{2} = 253[/tex]
Hence, the maximum possible number of handshakes that can happen at the party is 253.
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If Karel starts at Street 1 and Avenue 1, facing East, where will Karel be, and what direction will Karel be facing after running the following code? (Assume the world is 10x10 in size)move();turnLeft();putBall();turnLeft();turnLeft();turnLeft();move();turnLeft();
After running the given code, Karel will be at Street 2 and Avenue 2, facing North.
Here is a step-by-step explanation of what the code does:
move(); - Karel moves one block east, to Street 1 and Avenue 2.
turnLeft(); - Karel turns left to face north.
putBall(); - Karel puts a ball at Street 1 and Avenue 2.
turnLeft(); turnLeft(); turnLeft(); - Karel turns left three times to face south.
move(); - Karel moves one block south to Street 2 and Avenue 2.
turnLeft(); - Karel turns left to face east.
So after executing this code, Karel will be at Street 2 and Avenue 2, facing North.
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A savings account pays a 3% nominal annual interest rate and has a balance of $1,000. Any interest earned is deposited into the account and no further deposits or withdrawals are made. If interest is compounded semi-annually (every six months), what interest rate would be used for each calculation?
A. 3%
B. 2%
C. 1.5%
D. 12%
E. 18%
The answer is: C. 1.5%
Riley started selling bracelets. During the first month she sold 400 bracelets at $10 each. She tried raising the price, but for every $0. 50 she raised the price, she sold 8 fewer bracelets. What price should she charge in order to make the highest possible gross income?
$17.5 price should she charge in order to make the highest possible gross income.
Given two points are (400, 10) and (392, 10.5)
slope = (10.5-10)/(392 -400) = 0.5/ - 8 = -0.0625
Equation is
p -10 = -0.0625(x-400)
p-10 = -0.0625x + 25
p = -0.0625x + 35
find revenue as
R=x*p
-0.0625x² + 35x
To maximize,
R'(x) =0
-0.125x + 35 = 0
35/0.125 = x
280 = x
when x is equal to 280, find
p= -0.0625(280) + 35
p= -17.5 +35
p= 17.5
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Please help me with my math
Answer:
[tex]\textsf{$\boxed{\checkmark}\;\;y$-value\;of\;vertex\;is\;$-1$}[/tex]
[tex]\textsf{$\boxed{\checkmark}$\;\;Minimum\;value\;occurs\;at\;$y = -1$}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=x^2+8x+15[/tex]
As the given equation is quadratic with a positive leading coefficient, it is a parabola that opens upwards. Therefore, its vertex is its minimum point. This means that the minimum value of the range is the y-value of the vertex.
The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-value of the vertex of the given equation is:
[tex]\implies x=\dfrac{-8}{2(1)}=-4[/tex]
To find the y-value of the vertex, substitute x = -4 into the equation:
[tex]\begin{aligned}\implies y&=(-4)^2+8(-4)+15\\&=16-32+15\\&=-16+15\\&=-1\end{aligned}[/tex]
Therefore, the minimum y-value of the function is y = -1, so the range is y ≥ -1.
Therefore, the following are true statement about the given equation:
y-value of vertex is -1Minimum value occurs at y = -1out of total student 3/5 are girls .On a particular day one third boys and 2/5 girls were absent. If total absentees was 280 find total number of students
Answer:
Step-by-step explanation:
Calculate fraction of boys
If girls =3/5, then boys = 1 - 3/5 = 2/5.
Calculate fraction of students absent
Girls - 2/5 of 3/5 = 6/25
Boys - 1/3 of 2/5 = 2/15
6/25+2/15=28/75
Calculate total number of students
If 28/75 = 280
280/28=10
10x75=750
Total number of students = 750
Which of the following are key ingredients of a confidence interval based on the Central Limit Theorem?
(1) A summary statistic (e.g. a mean) from your sample
(2) A multiple z, based on a tail area from the normal distribution.
(3) A formula for the standard error of your summary statistic.
a. All of the above (1, 2, and 3)
b. (1) and (2)
c. (1) and (3)
d. (2) and (3)
Option a. (All of the above (1, 2, and 3)) is the right answer to the question regarding the key ingredients of a confidence interval based on the Central Limit Theorem.
A confidence interval is a statistical estimate of a population parameter with a level of confidence or certainty.
The Central Limit Theorem states that the distribution of the means of a sufficiently large sample size from a population with a finite variance will be approximately normal, regardless of the population's actual distribution.
A confidence interval based on the Central Limit Theorem, there are three key ingredients:
1. A summary statistic (e.g. a mean) from your sample
2. A multiple z, based on a tail area from the normal distribution.
3. A formula for the standard error of your summary statistic.
For a given level of confidence, the z-score corresponds to the number of standard deviations from the mean. The standard error of a summary statistic is a measure of the variability of the estimate that is dependent on the size of the sample, the variability of the population, and the type of summary statistic. The standard error of a sample mean is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.
Thus, all the above points (1, 2, and 3) are the key ingredients of a confidence interval based on the Central Limit Theorem.
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Make up a sequences that have (a) 3,3,3,3,... as its second differences. (b) 1, 2,3,4,5,... as its third differences (c) 1, 2, 4,8,16,... as its 100th differences.
The nth term of the sequence is 2^n.
(a) 3, 3, 3, 3, ... is a sequence that has 0 for both its first and second differences. That is, every term in the sequence is the same.(b) The sequence is the series of natural numbers. It has 0 for its first and second differences, and 6 for its third differences. The nth term of the sequence is n.(c) The sequence has 0 for its first 99 differences and 100! for its 100th difference. The nth term of the sequence is 2^n.
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The spinner above is used in a game. What is the theoretical probability of the given event with one spin?
P (5)
Answer:
B
Step-by-step explanation
so there is 8 numbers so when you spin you have a 1/8 chance of spinning the numberSolve each system of equations algebraically. y=x + 15, y= 2x
The solution to the system of equations is (15, 30).
What is system of equations?A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.
Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.
The given system of equations are y=x + 15, y= 2x.
Substitute the value of y from equation 2 in equation 1:
x + 15 = 2x
15 = x
Substitute the value of x to get the value of y:
y = 2x = 2(15) = 30
Hence, the solution to the system of equations is (15, 30).
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answer quickly please
Answer:
m = -3/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -2) (-3,2)
We see the y increase by 4 and the x decrease by 3, so the slope is
m = -3/4
the population of a country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1992. round your answer to 1 decimal place. the approximate population in 1992 is\
The population of the country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. Assuming that the population of the country continues to follow an exponential growth model, Rounding off the answer to one decimal place, the approximate population in 1992 is 348.2 million.
How to calculate the projected population? We are given, Population in 1982 = 259 millionTime taken = 10 years rate of growth = 1.6% = 0.016 (expressed as a decimal)The formula for exponential growth can be written as; Population = P0ert where, P0 is the initial population, e is the natural logarithmic base, r is the rate of growth and t is the time period We are required to find the projected population in 1992, which means the time period is 10 years (from 1982 to 1992).
Hence, substituting the given values in the formula, we get; P = 259e 0.016 × 10P = 259e0.16P = 259 × 1.185P = 307.215 million Hence, the projected population in 1992 is 307.215 million (rounded off to 1 decimal place, it is 307.2 million).
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I need help asap I just need atleast one of these explained and I can do the rest
Answer:
To factor 30b³-54b², we can factor out the greatest common factor of 6b² to get:
30b³-54b² = 6b²(5b-9)
To factor 35-48y³, we can notice that it is a difference of cubes:
35-48y³ = (5)³ - (4y)³ = (5-4y)(25+20y+16y²)
To factor x³+8, we can use the sum of cubes formula:
x³+8 = (x+2)(x²-2x+4)
To factor 3-64, we can use the difference of squares formula:
3-64 = (1)² - (8)² = (1+8)(1-8) = -7(-9) = 63
To factor 8c³+343, we can use the sum of cubes formula:
8c³+343 = (2c)^3 + 7³ = (2c+7)(4c²-14c+49)
To add or subtract complex polynomials, we simply combine like terms. For example:
(3x²+2x-5) + (4x²-3x+7) = 7x²-x+2
To multiply complex polynomials, we can use the distributive property and FOIL method. For example:
(2x+1)(3x-4) = 6x²-5x-4
To factor complex polynomials, we can use various methods such as factoring out the greatest common factor, using the difference of squares formula, using the sum or difference of cubes formula, or factoring by grouping.
The formulas provided are for factoring the sum or difference of cubes:
(a + b³) = (a + b)(a² - ab + b²)(a - b³) = (a - b)(a² + ab + b²)These formulas can be useful for factoring complex polynomials that have a cube term or a constant term in addition to the quadratic and linear terms.
when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)
The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.
What is the probability of randomly selected component?We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.
We need to find the probability that a randomly selected component is shorter than 7 inches long.
We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:
z = (7 - 8) / 1.5 = -0.67
Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:
P(z < -0.67) = 0.2514
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Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}
An appropriate theorem to show that the given set, W, is a vector space. A specific example can be
[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s and 3p = -2s - 3r
Sets represent values that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.
The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.
The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.
The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.
Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is
S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties
u +v =y+ u and (u + v)+w=u + (v +W).
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if belongs to the interval , at which values of does the curve have a tangent line parallel to the line ?
Answer:
you need to show the numbers
Step-by-step explanation:
suppose that 78% of all dialysis patients will survive for at least 5 years. in a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?
The probability that the 78% of all the dialysis patients survive for at least five years will exceed 80%, rounded to 5 decimal places is 0.3192.
What is the probability?The proportion of dialysis patients surviving for at least 5 years = 78% = 0.78
Assuming that a simple random sample of 100 dialysis patients is selected, the sample size is n = 100.
Let p be the proportion of dialysis patients in the sample surviving for at least 5 years.
Then, the sample mean is given by:
μp = E(p) = p = 0.78
So, the mean proportion of dialysis patients surviving for at least 5 years is equal to 0.78.
The standard error of the sample proportion is given by:
σp=√p(1−p)/n
σp=√0.78(1−0.78)/100
σp=0.04278
The required probability is to find P(p > 0.80):
P(p > 0.80) = P(Z > (0.80 - 0.78)/0.04278)
P(p > 0.80) = P(Z > 0.467) = 1 - P(Z < 0.467) = 1 - 0.6808 = 0.3192 (rounded to 5 decimal places)
Therefore, the probability that the proportion surviving for at least five years will exceed 80% in a simple random sample of 100 new dialysis patients is 0.3192.
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In the diagram below what is the measure in angel x
Answer:
143°
When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.
#Brainlist! Help! Will! Make! You! Brainlist!
Show all steps and how you got the answer
Answer:
x = 8500
y = 15000
Step-by-step explanation:
small vans: x
large vans: y
A: 5x + 2y = 72500
B: 2x + 6y = 107000
5x + 2y = 72500 => y = (72500 - 5x)/2
2x + 6(72500 - 5x)/2 = 107000
2x + 217500 - 15x = 107000
15x - 2x = 217500 - 107000
13x = 110500
x = 110500/13 = 8500
y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000
The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:
The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].
What is Hypothesis test?Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.
Using the appropriate notation, the hypotheses can be expressed as:
$H_0: p = 0.08$
$H_a: p < 0.08$
Therefore, the appropriate set of hypotheses for the mayor's significance test are:
[tex]$$H_0: p = 0.08$$[/tex]
[tex]$$H_a: p < 0.08$$[/tex]
Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate
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find the long leg: b =
Answer:
b ≈ 12.1
Step-by-step explanation:
using the tangent ratio in the right triangle
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )
7 × tan60° = b , then
b ≈ 12.1 ( to the nearest tenth )
venus is known as the ''cloudy planet'' because it is covered with thick, yelllow clouds. The gravity of venus is 90% of earths gravity. To calculate your weight on venus, multiply your weight by 0.9
Answer:
Step-by-step explanation:
How does Priestley present the theme of social class in Act 1? 3 paragraphs 80 POINTS!!!
INTRODUCTION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
PARAGRAPH 1 -
PARAGRAPH 2-
PARAGRAPH 3-
CONCLUSION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
could someone help out?
Answer:
27.18
Step-by-step explanation:
Firstly, you must label the triangle.
r- opposite
13.85- adjacent
We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.
tan (63) = r/13.85
Then, times 13.85 on both sides so we only have our unknown on one side.
(x13.85) tan(63)= r/13.85 (x13.85)
r= tan (63) x 13.85
r=27.18
:)
Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour
(mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the predicted fuel
efficiency for a speed of 30 mph?
17.67 mpg
26.50 mpg
30.00 mpg
37.74 mpg
The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:
26.50 mpg.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).
The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:
In(Fuel Efficiency) = 1.437 + 0.541 x In(30).
In(Fuel Efficiency) = 3.277.
The exponential is the inverse of the ln, hence:
Fuel Efficiency = e^3.277
Fuel Efficiency = 26.50 mpg.
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A friend is building a garden with two side lengths 16 ft and exactly one right angle. What geometric figures could describe how the garden might look?
SELECT ALL THAT APPLY:
A. Kite.
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
(Remember it is multiple choice)
Answer:
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
Step-by-step explanation:
Answer:
The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.
Six more than the quotient of a number and 8 is equal to 4
use the variable x for the unknown number
!!!TRANSLATE INTO A EQUATION!!!
Answer:
x/8 + 6 = 4
Step-by-step explanation:
x / 8 + 6 = 4
x/8 = -2
x = 8*-2 = -16.
Let f be a differentiable function defined by f(x) = 3x + 2e −3x , and let g be a differentiable function with derivative given by g′(x) = 1 x + 4. It is known that lim g(x) = [infinity].
x→[infinity]
The value of lim f(x) g(X) is:______
x→[infinity]
The value of lim f(x)g(x) as x approaches infinity is 0.
L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.
To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:
lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]
= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]
Applying L'Hopital's rule to the fraction in the numerator, we get:
lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]
= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]
= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]
= 0
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This is Section 3.2 Problem 2: The cost function, in dollars, for producing $x$ items of a certain brand of barstool is given by C(x)-0.01x3-0.6x2+13x+200 (a) C(x).03r- .12x +13 (b) MC(50)-82 dollars per barstool . It approximately represents the cost of producing the 50 th barstool (c) The exact cost of producing the 51th barstool is C 51 -c50 28.91 dollars (d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately -Select
In the following question, the Total cost to production 50 barstools: $1,200 Total cost to produce 51 barstools: $1,228.91 "Total cost to produce 52 barstools: $1,258.44" Total cost to produce 53 barstools: $1,288.59 Therefore, the approximate total cost of producing 53 barstools is $559.15.
The cost function for producing $x$ items of a certain brand of barstool is given by C(x)=0.01x3-0.6x2+13x+200.
(a) C(x)=0.03x3- 0.12x2+13
(b) MC(50)=-82 dollars per barstool.
It approximately represents the cost of producing the 50th barstool.
(c) The exact cost of producing the 51st barstool is C51=C50+MC(50)=$28.91 dollars.
(d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately C50+(53-50) MC(50)=$229.82.
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Graph the system of equations {y=−12x+4y=−12x−2
Answer:
Step-by-step explanation: i hope this help if not let me know so i can fix it
I’m a bit stuck please help me out
On solving the question we can say that Therefore, the solutions to the inequality given inequality are: x < 4 or x > 6.
What is inequality?An inequality in mathematics is a relationship between two expressions or values that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality.
two inequalities
4x - 6 < 10
4x < 16
x < 4
2x - 4 > 8
2x > 12
x > 6
Therefore, the solutions to the given inequality are:
x < 4 or x > 6.
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