# How do you solve -\frac { 242} { 21} = - \frac { 9} { 4} x + \frac { 1} { 3} - 8?

Jun 12, 2017

$x = 1 \frac{5}{7}$

#### Explanation:

-242/21 color(red)(+ 8) = -9/4 x + 1/3 color(red)(cancel(color(black)(- 8) color(red)( + 8)

$- 11 \frac{11}{21} + 8 = - \frac{9}{4} x + \frac{1}{3}$

-3 11/21 -1/3 = -9/4 x color(red)(cancel( color(black)(+ 1/3) color(red)(-1/3)

$- 3 \frac{11}{21} - \frac{7}{21} = - \frac{9}{4} x$

$- 3 \frac{18}{21} = - \frac{9}{4} x$

-3 6/7 color(red)(÷ -9/4)= color(red)(cancel(color(black)(-9/4) color(red)(÷ -9/4)) x

x = -3 6/7 ÷ -9/4

$x = - 3 \frac{6}{7} \times - \frac{4}{9}$

color(blue)(x = 1 5/7

We can now substitute $1 \frac{5}{7}$ for $x$ in the equation to prove our answer.

$- \frac{242}{21} = - \frac{9}{4} x + \frac{1}{3} - 8$

$- \frac{242}{21} = - \frac{9}{4} \times 1 \frac{5}{7} + \frac{1}{3} - 8$

$- \frac{242}{21} = - 3 \frac{6}{7} + \frac{1}{3} - 8$

$- \frac{242}{21} = - 3 \frac{11}{21} - 8$

$- \frac{242}{21} = - 11 \frac{11}{21}$

$- \frac{242}{21} = - \frac{242}{21}$