Solve -4(2-x)=4/5(x+38)

$$- 4 ( 2 - x ) = \frac { 4 } { 5 } ( x + 38 )$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Use the distributive property to multiply -4 by 2-x.

$$-8+4x=\frac{4}{5}\left(x+38\right)$$

Use the distributive property to multiply \frac{4}{5} by x+38.

$$-8+4x=\frac{4}{5}x+\frac{4}{5}\times 38$$

Express \frac{4}{5}\times 38 as a single fraction.

$$-8+4x=\frac{4}{5}x+\frac{4\times 38}{5}$$

Multiply 4 and 38 to get 152.

$$-8+4x=\frac{4}{5}x+\frac{152}{5}$$

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

$$-8+4x-\frac{4}{5}x=\frac{152}{5}$$

Combine 4x and -\frac{4}{5}x to get \frac{16}{5}x.

$$-8+\frac{16}{5}x=\frac{152}{5}$$

Add 8 to both sides.

$$\frac{16}{5}x=\frac{152}{5}+8$$

Convert 8 to fraction \frac{40}{5}.

$$\frac{16}{5}x=\frac{152}{5}+\frac{40}{5}$$

Since \frac{152}{5} and \frac{40}{5} have the same denominator, add them by adding their numerators.

$$\frac{16}{5}x=\frac{152+40}{5}$$

Add 152 and 40 to get 192.

$$\frac{16}{5}x=\frac{192}{5}$$

Multiply both sides by \frac{5}{16}, the reciprocal of \frac{16}{5}.

$$x=\frac{192}{5}\times \frac{5}{16}$$

Multiply \frac{192}{5} times \frac{5}{16} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{192\times 5}{5\times 16}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{192}{16}$$

Divide 192 by 16 to get 12.

$$x=12$$