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

Jan 29, 2017

m = -7

#### Explanation:

Multiply both sides by 9. This gives us
$\frac{9}{9} \left(2 m - 16\right) = \frac{9}{3} \left(2 m + 4\right)$

which simplifies to

$2 m - 16 = 3 \left(2 m + 4\right)$

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

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

which simplifies to

$2 m = 6 m + 28$

subtract 6m from both sides

$2 m - 6 m = 6 m + 28 - 6 m$

which simplifies to

$- 4 m = 28$

Divide both sides by -4

$\left(\frac{- 4}{- 4}\right) m = \frac{28}{- 4}$

which gives us

$m = - 7$

Verification
Left hand side

$\left(\frac{1}{9}\right) \left(\left(2 \cdot - 7\right) - 16\right)$
$\left(\frac{1}{9}\right) \left(- 14 - 16\right)$
$\left(\frac{1}{9}\right) \left(- 30\right)$
$- \frac{30}{9}$
$- \frac{10}{3}$

Right Hand Side
(1/3)((2 * -7) + 4))
$\left(\frac{1}{3}\right) \left(- 14 + 4\right)$
$\left(\frac{1}{3} \left(- 10\right)\right)$
$- \frac{10}{3}$

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