How do you solve $\frac{1}{9} (2 m - 16) = \frac{1}{3} (2 m + 4)$ $1/9(2m-16)=1/3(2m+4)$ ?

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How do you solve $\frac{1}{9} (2 m - 16) = \frac{1}{3} (2 m + 4)$ $1/9(2m-16)=1/3(2m+4)$ ?

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Answer 1 · 2017-01-29T15:33:38

m = -7

Explanation:

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

which simplifies to

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

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

Add 16 to both sides

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

which simplifies to

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

subtract 6m from both sides

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

which simplifies to

$- 4 m = 28$ $-4m = 28$

Divide both sides by -4

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

which gives us

$m = - 7$ $m = -7$

Verification
Left hand side

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

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

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

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How do you solve $\frac{1}{9} (2 m - 16) = \frac{1}{3} (2 m + 4)$ $1/9(2m-16)=1/3(2m+4)$ ?

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