Question

Distribute and combine like terms. Please show all of your work.

-5(3x + 7) - 4(x - 4) + 11

Answer 1

Answer: 19x - 8

Steps

-5(3x + 7)

Apply the distributive law: a( b + c ) = ab + ac

a = -5, b = 3x, c = 7

= -5 * 3x + (-5) x 7

Apply minus - plus rules

+(-a) = -a

= -5 * 3x - 5 x 7

Simplify

-5 * 3x - 5 x 7

Multiply the numbers: 5 x 3 = 15

= -15x - 5 x 7

Multiply the numbers: 5 x 7 = 35

= -15x - 35

Plug in the values

-15x - 35 - 4(x - 4) + 11

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-4(x - 4)

Apply the distributive law: a( b - c ) = ab - ac

a = -4, b = x, c = 4

= -4x - (-4) * 4

Apply minus - plus rules

-(-a) = a

= -4x + 4 * 4

Multiply the numbers: 4 * 4 = 16

= -4x + 16

Plug in the values

-15x - 35 - 4x + 16 + 11

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Simplify

-15x - 35 - 4x + 16 + 11

Group like terms

= -15x - 4x - 35 + 16 + 11

Add similar elements: -15x - 4x = -19x

= -19x - 35 + 16 + 11

Add/Subtract the numbers: -35 + 16 + 11 = -8

= 19x - 8

Answer 2

For this case we have the following expression:

`-5 (3x + 7) -4 (x-4) +11`

For simplicity we follow the steps:

We apply distributive property to the terms within the parenthesis, bearing in mind that:

`- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =`

We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

`-15x-4x-35 + 16 + 11 =\\-19x-8`

ANswer:

`-19x-8`