Solve 90^circ-x=2/3(180^circ-x)-45^circ

$$90 ^ { \circ } - x = \frac { 2 } { 3 } ( 180 ^ { \circ } - x ) - 45 ^ { \circ }$$

Solve for x

$$x=45$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 180-x.

$$90-x=\frac{2}{3}\times 180+\frac{2}{3}\left(-1\right)x-45$$

Express \frac{2}{3}\times 180 as a single fraction.

$$90-x=\frac{2\times 180}{3}+\frac{2}{3}\left(-1\right)x-45$$

Multiply 2 and 180 to get 360.

$$90-x=\frac{360}{3}+\frac{2}{3}\left(-1\right)x-45$$

Divide 360 by 3 to get 120.

$$90-x=120+\frac{2}{3}\left(-1\right)x-45$$

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

$$90-x=120-\frac{2}{3}x-45$$

Subtract 45 from 120 to get 75.

$$90-x=75-\frac{2}{3}x$$

Add \frac{2}{3}x to both sides.

$$90-x+\frac{2}{3}x=75$$

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

$$90-\frac{1}{3}x=75$$

Subtract 90 from both sides.

$$-\frac{1}{3}x=75-90$$

Subtract 90 from 75 to get -15.

$$-\frac{1}{3}x=-15$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=-15\left(-3\right)$$

Multiply -15 and -3 to get 45.

$$x=45$$