Solve x-10=5/9(x-2)

$$x - 10 = \frac { 5 } { 9 } ( x - 2 )$$

Solve for x

$$x=20$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{9} by x-2.

$$x-10=\frac{5}{9}x+\frac{5}{9}\left(-2\right)$$

Express \frac{5}{9}\left(-2\right) as a single fraction.

$$x-10=\frac{5}{9}x+\frac{5\left(-2\right)}{9}$$

Multiply 5 and -2 to get -10.

$$x-10=\frac{5}{9}x+\frac{-10}{9}$$

Fraction \frac{-10}{9} can be rewritten as -\frac{10}{9} by extracting the negative sign.

$$x-10=\frac{5}{9}x-\frac{10}{9}$$

Subtract \frac{5}{9}x from both sides.

$$x-10-\frac{5}{9}x=-\frac{10}{9}$$

Combine x and -\frac{5}{9}x to get \frac{4}{9}x.

$$\frac{4}{9}x-10=-\frac{10}{9}$$

Add 10 to both sides.

$$\frac{4}{9}x=-\frac{10}{9}+10$$

Convert 10 to fraction \frac{90}{9}.

$$\frac{4}{9}x=-\frac{10}{9}+\frac{90}{9}$$

Since -\frac{10}{9} and \frac{90}{9} have the same denominator, add them by adding their numerators.

$$\frac{4}{9}x=\frac{-10+90}{9}$$

Add -10 and 90 to get 80.

$$\frac{4}{9}x=\frac{80}{9}$$

Multiply both sides by \frac{9}{4}, the reciprocal of \frac{4}{9}.

$$x=\frac{80}{9}\times \frac{9}{4}$$

Multiply \frac{80}{9} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{80\times 9}{9\times 4}$$

Cancel out 9 in both numerator and denominator.

$$x=\frac{80}{4}$$

Divide 80 by 4 to get 20.

$$x=20$$