Answer:
[tex]x = -20[/tex]
Step-by-step explanation:
Starting with:
[tex]3(x + 8) = -3(7 - \frac{1}{4}x)[/tex]
Use distributive property to multply 3 by X + 8
[tex]3x + 24 = -3(7-\frac{1}{4} x)[/tex]
Use distributive property to multiply -3 by 7 - 1/4x
[tex]3x + 24 = -21 - 3(-\frac{1}{4})x[/tex]
Express [tex]-3(\frac{1}{4} )[/tex] as a single fraction.
[tex]3x + 24 = -21 + \frac{- 3(-1)}{4}x[/tex]
Multiply -3 and -1 to get 3
[tex]3x + 24 = -21 + \frac{3}{4}x[/tex]
Subtract [tex]\frac{3}{4} x[/tex] from both sides
[tex]3x + 24 - \frac{3}{4}x= -21[/tex]
Combine 3x and [tex]-\frac{3}{4}x[/tex] to get [tex]\frac{9}{4} x[/tex]
[tex]\frac{9}{4} x + 24 = -21[/tex]
Subtract 24 from both sides
[tex]\frac{9}{4}x = -21 - 24[/tex]
Subtract 24 from -21 to get -45
[tex]\frac{9}{4}x = -45[/tex]
Multiply both sides by [tex]\frac{4}{9}[/tex], the reciprocal of [tex]\frac{9}{4}[/tex]
[tex]x = -45 * (\frac{4}{9})[/tex]
Express it as a single fraction
[tex]x = \frac{-45 * 4}{9}[/tex]
Multiply the top to get -180
[tex]x = \frac{-180}{9}[/tex]
Divide -180 by 9 and get -20
[tex]x = -20[/tex]
