Solve x-9=2/3(x-5)

$$x - 9 = \frac { 2 } { 3 } ( x - 5 )$$

Solve for x

$$x=17$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x-5.

$$x-9=\frac{2}{3}x+\frac{2}{3}\left(-5\right)$$

Express \frac{2}{3}\left(-5\right) as a single fraction.

$$x-9=\frac{2}{3}x+\frac{2\left(-5\right)}{3}$$

Multiply 2 and -5 to get -10.

$$x-9=\frac{2}{3}x+\frac{-10}{3}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$x-9=\frac{2}{3}x-\frac{10}{3}$$

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

$$x-9-\frac{2}{3}x=-\frac{10}{3}$$

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

$$\frac{1}{3}x-9=-\frac{10}{3}$$

Add 9 to both sides.

$$\frac{1}{3}x=-\frac{10}{3}+9$$

Convert 9 to fraction \frac{27}{3}.

$$\frac{1}{3}x=-\frac{10}{3}+\frac{27}{3}$$

Since -\frac{10}{3} and \frac{27}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x=\frac{-10+27}{3}$$

Add -10 and 27 to get 17.

$$\frac{1}{3}x=\frac{17}{3}$$

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

$$x=\frac{17}{3}\times 3$$

Cancel out 3 and 3.

$$x=17$$