Solve -8(5-x)=4/5(x+13)

$$- 8 ( 5 - x ) = \frac { 4 } { 5 } ( x + 13 )$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply -8 by 5-x.

$$-40+8x=\frac{4}{5}\left(x+13\right)$$

Use the distributive property to multiply \frac{4}{5} by x+13.

$$-40+8x=\frac{4}{5}x+\frac{4}{5}\times 13$$

Express \frac{4}{5}\times 13 as a single fraction.

$$-40+8x=\frac{4}{5}x+\frac{4\times 13}{5}$$

Multiply 4 and 13 to get 52.

$$-40+8x=\frac{4}{5}x+\frac{52}{5}$$

Subtract \frac{4}{5}x from both sides.

$$-40+8x-\frac{4}{5}x=\frac{52}{5}$$

Combine 8x and -\frac{4}{5}x to get \frac{36}{5}x.

$$-40+\frac{36}{5}x=\frac{52}{5}$$

Add 40 to both sides.

$$\frac{36}{5}x=\frac{52}{5}+40$$

Convert 40 to fraction \frac{200}{5}.

$$\frac{36}{5}x=\frac{52}{5}+\frac{200}{5}$$

Since \frac{52}{5} and \frac{200}{5} have the same denominator, add them by adding their numerators.

$$\frac{36}{5}x=\frac{52+200}{5}$$

Add 52 and 200 to get 252.

$$\frac{36}{5}x=\frac{252}{5}$$

Multiply both sides by \frac{5}{36}, the reciprocal of \frac{36}{5}.

$$x=\frac{252}{5}\times \frac{5}{36}$$

Multiply \frac{252}{5} times \frac{5}{36} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{252\times 5}{5\times 36}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{252}{36}$$

Divide 252 by 36 to get 7.

$$x=7$$