Please help me! I'm stuck and really confused, thank you so much!

Answer:

(a) [tex]5 * (2x - 1) = 10x - 5[/tex]

(b) [tex]6 * x = x + 2x + 3x[/tex]

(c) [tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - 3[/tex]

(d) [tex]y(3x + 4z) = 3xy + 4yz[/tex]

(e) [tex]z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz[/tex]

Step-by-step explanation:

Solving (a):

Given

[tex]10x - 5[/tex]

Required

Express as a product

Express 10x as 5 * 2x

[tex]10x - 5 = 5 * 2x - 5[/tex]

Apply distributive property

[tex]10x - 5 = 5(2x - 1)[/tex]

[tex]10x - 5 = 5 * (2x - 1)[/tex]

So:

[tex]5 * (2x - 1) = 10x - 5[/tex]

Solving (b):

Given

[tex]x + 2x + 3x[/tex]

Required

Express as a product

Express 2x and 3x as 2 * x and 3 * x, respectively

[tex]x + 2x + 3x = x + 2*x + 3*x[/tex]

Apply distributive property

[tex]x + 2x + 3x = x(1 + 2 + 3)[/tex]

[tex]x + 2x + 3x = x(6)[/tex]

[tex]x + 2x + 3x = 6*x[/tex]

So:

[tex]6 * x = x + 2x + 3x[/tex]

Solving (c):

Given

[tex]\frac{1}{2}(x - 6)[/tex]

Required

Express as a sum/difference

Apply distributive property

[tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - \frac{1}{2}*6[/tex]

[tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - \frac{6}{2}[/tex]

[tex]\frac{1}{2}(x - 6) = \frac{1}{2}x - 3[/tex]

Solving (d):

Given

[tex]y(3x + 4z)[/tex]

Required

Express as a sum/difference

Apply distributive property

[tex]y(3x + 4z) = 3x * y + 4z * y[/tex]

[tex]y(3x + 4z) = 3xy + 4yz[/tex]

Solving (e):

Given

[tex]2xyz - 3yz + 4xz[/tex]

Required

Express as a product

Factorize

[tex]2xyz - 3yz + 4xz = 2xy * z - 3y * z + 4x * z[/tex]

Apply distributive property

[tex]2xyz - 3yz + 4xz = z(2xy - 3y + 4x)[/tex]

So:

[tex]z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz[/tex]

Please help me with this!

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A. x + 5 = 5 + x
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associative
commutative
distributive

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transitive
commutative
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associative
..........................................................................
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