Solve 1/3(x+6)=2/3(x-9)

$$\frac { 1 } { 3 } ( x + 6 ) = \frac { 2 } { 3 } ( x - 9 )$$

Solve for x

$$x=24$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x+6.

$$\frac{1}{3}x+\frac{1}{3}\times 6=\frac{2}{3}\left(x-9\right)$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$\frac{1}{3}x+\frac{6}{3}=\frac{2}{3}\left(x-9\right)$$

Divide 6 by 3 to get 2.

$$\frac{1}{3}x+2=\frac{2}{3}\left(x-9\right)$$

Use the distributive property to multiply \frac{2}{3} by x-9.

$$\frac{1}{3}x+2=\frac{2}{3}x+\frac{2}{3}\left(-9\right)$$

Express \frac{2}{3}\left(-9\right) as a single fraction.

$$\frac{1}{3}x+2=\frac{2}{3}x+\frac{2\left(-9\right)}{3}$$

Multiply 2 and -9 to get -18.

$$\frac{1}{3}x+2=\frac{2}{3}x+\frac{-18}{3}$$

Divide -18 by 3 to get -6.

$$\frac{1}{3}x+2=\frac{2}{3}x-6$$

Subtract \frac{2}{3}x from both sides.

$$\frac{1}{3}x+2-\frac{2}{3}x=-6$$

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

$$-\frac{1}{3}x+2=-6$$

Subtract 2 from both sides.

$$-\frac{1}{3}x=-6-2$$

Subtract 2 from -6 to get -8.

$$-\frac{1}{3}x=-8$$

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

$$x=-8\left(-3\right)$$

Multiply -8 and -3 to get 24.

$$x=24$$