Question

4[5-8(4c-3)]=12(1-13c)-8

Answer 1

`\boxed{c = -4}`

First, we will use the distributive property (order of operations) to simplify the equation:

(4)(5) + (4)(−8(4c−3)) = (12)(1) + (12)(−13c)+ (−8) =

20 + (−128c) + 96 = 12 + (−156c)+ (−8)

Now, we will combine like terms to simplify the equation:

(−128c) + (20 + 96) = (−156c) + (12+ (−8) =

−128c + 116 = −156c + 4

Now we will add 156 to both sides, using inverse operations.

−128c + 116 + 156c = −156c + 4 + 156c =

28c + 116 = 4

Now we will subtract 116 from both sides:

28c + 116 − 116 = 4 − 116 =

28c = −112

Lastly, we will divide both sides by 28:

28c/28 = c

-112/28 = -4

The equation now looks like:

c = -4

Therefore, your answer is -4.

Answer 2

Hi there! Hopefully this helps!

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Answer:
`\boxed{c = -4}`

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`4(5-8(4c-3))=12(1-13c)-8`

Use the distributive property to multiply −8 by 4c − 3.

`4(5-32c+24)=12(1-13c)-8`

Add 5 and 24 to get 29.

`4(29 - 32c)=12(1-13c)-8`

Use the distributive property to multiply 4 by 29 − 32c.

`116-128c=12(1-13c)-8`

Use the distributive property to multiply 12 by 1 − 13c.

`116-128c=12-156c-8`

Subtract 8 from 12 to get 4.

`116-128c=4-156c`

Add 156c to both sides.

`116 - 128c+156c=4`

Combine −128c and 156c to get 28c.

`116+28c=4`

Subtract 116 from both sides.

`28c=4-116`

Subtract 116 from 4 to get −112.

`28c=-112`

Divide both sides by 28.

`c=(-112)/(28)`

Divide −112 by 28 to get, you guessed it, -4!