Solve 90-x=2/5(180-x)

$$90 - x = \frac { 2 } { 5 } ( 180 - x )$$

Solve for x

$$x=30$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by 180-x.

$$90-x=\frac{2}{5}\times 180+\frac{2}{5}\left(-1\right)x$$

Express \frac{2}{5}\times 180 as a single fraction.

$$90-x=\frac{2\times 180}{5}+\frac{2}{5}\left(-1\right)x$$

Multiply 2 and 180 to get 360.

$$90-x=\frac{360}{5}+\frac{2}{5}\left(-1\right)x$$

Divide 360 by 5 to get 72.

$$90-x=72+\frac{2}{5}\left(-1\right)x$$

Multiply \frac{2}{5} and -1 to get -\frac{2}{5}.

$$90-x=72-\frac{2}{5}x$$

Add \frac{2}{5}x to both sides.

$$90-x+\frac{2}{5}x=72$$

Combine -x and \frac{2}{5}x to get -\frac{3}{5}x.

$$90-\frac{3}{5}x=72$$

Subtract 90 from both sides.

$$-\frac{3}{5}x=72-90$$

Subtract 90 from 72 to get -18.

$$-\frac{3}{5}x=-18$$

Multiply both sides by -\frac{5}{3}, the reciprocal of -\frac{3}{5}.

$$x=-18\left(-\frac{5}{3}\right)$$

Express -18\left(-\frac{5}{3}\right) as a single fraction.

$$x=\frac{-18\left(-5\right)}{3}$$

Multiply -18 and -5 to get 90.

$$x=\frac{90}{3}$$

Divide 90 by 3 to get 30.

$$x=30$$