Solve 90-x=1/3(180-x)-10

$$90-x= \frac{ 1 }{ 3 } (180-x)-10$$

Solve for x

$$x=60$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 180-x.

$$90-x=\frac{1}{3}\times 180+\frac{1}{3}\left(-1\right)x-10$$

Multiply \frac{1}{3} and 180 to get \frac{180}{3}.

$$90-x=\frac{180}{3}+\frac{1}{3}\left(-1\right)x-10$$

Divide 180 by 3 to get 60.

$$90-x=60+\frac{1}{3}\left(-1\right)x-10$$

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

$$90-x=60-\frac{1}{3}x-10$$

Subtract 10 from 60 to get 50.

$$90-x=50-\frac{1}{3}x$$

Add \frac{1}{3}x to both sides.

$$90-x+\frac{1}{3}x=50$$

Combine -x and \frac{1}{3}x to get -\frac{2}{3}x.

$$90-\frac{2}{3}x=50$$

Subtract 90 from both sides.

$$-\frac{2}{3}x=50-90$$

Subtract 90 from 50 to get -40.

$$-\frac{2}{3}x=-40$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x=-40\left(-\frac{3}{2}\right)$$

Express -40\left(-\frac{3}{2}\right) as a single fraction.

$$x=\frac{-40\left(-3\right)}{2}$$

Multiply -40 and -3 to get 120.

$$x=\frac{120}{2}$$

Divide 120 by 2 to get 60.

$$x=60$$