Question

Which of the following equations has a solution x = 4? Select all that apply.

0-2 (32 – 4) = -16
{(100 + 2) = 6
20 - 15x = 6 - 2 (4x + 7)
(90 - 12) +6 = -10

Answer 1

Answer: 1st and 3rd

Explanation:

Answer 2

`-2(3x - 4) = -16` and
`20- 15x = 6 - 2(4x + 7)`

Explanation:

Given

`-2(3x - 4) = -16`

`(1)/(2)(10x + 2) = 6`

`20- 15x = 6 - 2(4x + 7)`

`(1)/(3)(9x - 12) + 6=-10`

Required

Equations with
`x = 4` as a solution

`-2(3x - 4) = -16`

Divide both sides by -2

`3x - 4 = 8`

Add 4 to both sides

`3x - 4 +4= 8+4`

`3x =12`

Divide both sides by 3

`x = 4`

`(1)/(2)(10x + 2) = 6`

Multiply both sides by 2

`10x + 2 = 12`

Subtract 2 from both sides

`10x + 2 -2= 12-2`

`10x = 10`

Divide both sides by 1

`x = 1`

`20- 15x = 6 - 2(4x + 7)`

Open bracket

`20 - 15x = 6 - 8x - 14`

Collect like terms

`8x - 15x = 6 - 14 - 20`

`-7x = -28`

Divide both sides by -7

`x = 4`

`(1)/(3)(9x - 12) + 6=-10`

Subtract 6 from both sides

`(1)/(3)(9x - 12) + 6-6=-10-6`

`(1)/(3)(9x - 12) =-16`

Multiply both sides by 3

`9x - 12 = -48`

Add 12 to both sides

`9x - 12 +12= -48+12`

`9x = -36`

Divide both sides by 4

`x =-4`

`-2(3x - 4) = -16` and
`20- 15x = 6 - 2(4x + 7)` have
`x = 4` has a solution