Solve 90-x+40=2/3(180-x)

$$90-x+40= \frac{ 2 }{ 3 } (180-x)$$

Solve for x

$$x=30$$

Steps for Solving Linear Equation

Add 90 and 40 to get 130.

$$130-x=\frac{2}{3}\left(180-x\right)$$

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

$$130-x=\frac{2}{3}\times 180+\frac{2}{3}\left(-1\right)x$$

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

$$130-x=\frac{2\times 180}{3}+\frac{2}{3}\left(-1\right)x$$

Multiply 2 and 180 to get 360.

$$130-x=\frac{360}{3}+\frac{2}{3}\left(-1\right)x$$

Divide 360 by 3 to get 120.

$$130-x=120+\frac{2}{3}\left(-1\right)x$$

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

$$130-x=120-\frac{2}{3}x$$

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

$$130-x+\frac{2}{3}x=120$$

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

$$130-\frac{1}{3}x=120$$

Subtract 130 from both sides.

$$-\frac{1}{3}x=120-130$$

Subtract 130 from 120 to get -10.

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

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

$$x=-10\left(-3\right)$$

Multiply -10 and -3 to get 30.

$$x=30$$