# How do you solve \frac { 8( 6- z ) } { 7} = - z?

Apr 11, 2018

Hi,
z = 48

#### Explanation:

$8 \frac{6 - z}{7}$ = -z (divide by 8)
$\frac{6 - z}{7}$ = $- \frac{1}{8}$z (multiply by 7)
$\left(6 - z\right)$ = $- \frac{7}{8}$z (all elements with z into one side)
$- z + \frac{7}{8} z$ = $- 6$
$- \frac{1}{8} z = - 6$ (multiply by -8)
$z = \left(- 6\right) \cdot \left(- 8\right) = 48$

Apr 11, 2018

$48$

#### Explanation:

Start by multiplying both sides by $7$ and distribute:

$\frac{8 \left(6 - z\right)}{7} = - z$

$8 \left(6 - z\right) = 7 \left(- z\right)$

$48 - 8 z = - 7 z$

Now add $8 z$ to both sides.

$48 \cancel{- 8 z + 8 z} = - 7 z + 8 z$

$48 = z$