Question

How do you solve `1/9(2m-16)=1/3(2m+4)`?

Answer 1

m = -7

Explanation:

Multiply both sides by 9. This gives us
`9/9 (2m -16) = 9/3(2m + 4)`

which simplifies to

`2m - 16 = 3(2m + 4)`

Simplify the right hand side by multiplying each element by 3
`2m - 16 = 6m + 12`

Add 16 to both sides

`2m - 16 + 16 = 6m + 12 + 16`

which simplifies to

`2m = 6m + 28`

subtract 6m from both sides

`2m - 6m = 6m + 28 - 6m`

which simplifies to

`-4m = 28`

Divide both sides by -4

`((-4)/(-4))m = (28)/(-4)`

which gives us

`m = -7`

Verification
Left hand side

`(1/9)((2 * -7) -16)`
`(1/9)(-14 -16)`
`(1/9)(-30)`
`-30/9`
`-10/3`

Right Hand Side
`(1/3)((2 * -7) + 4))`
`(1/3)(-14 + 4)`
`(1/3(-10))`
`-10/3`

Left side = Right side, proving our answer (m = -7) to be correct.