Solve 1/3(80-x)=90-x

$$\frac { 1 } { 3 } ( 80 - x ) = 90 - x$$

Solve for x

$$x=95$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 80-x.

$$\frac{1}{3}\times 80+\frac{1}{3}\left(-1\right)x=90-x$$

Multiply \frac{1}{3} and 80 to get \frac{80}{3}.

$$\frac{80}{3}+\frac{1}{3}\left(-1\right)x=90-x$$

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

$$\frac{80}{3}-\frac{1}{3}x=90-x$$

Add x to both sides.

$$\frac{80}{3}-\frac{1}{3}x+x=90$$

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

$$\frac{80}{3}+\frac{2}{3}x=90$$

Subtract \frac{80}{3} from both sides.

$$\frac{2}{3}x=90-\frac{80}{3}$$

Convert 90 to fraction \frac{270}{3}.

$$\frac{2}{3}x=\frac{270}{3}-\frac{80}{3}$$

Since \frac{270}{3} and \frac{80}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}x=\frac{270-80}{3}$$

Subtract 80 from 270 to get 190.

$$\frac{2}{3}x=\frac{190}{3}$$

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

$$x=\frac{190}{3}\times \frac{3}{2}$$

Multiply \frac{190}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{190\times 3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{190}{2}$$

Divide 190 by 2 to get 95.

$$x=95$$