Solve 3/4(x-10)=4/5x-20

$$\frac { 3 } { 4 } ( x - 10 ) = \frac { 4 } { 5 } x - 20$$

Solve for x

$$x=250$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by x-10.

$$\frac{3}{4}x+\frac{3}{4}\left(-10\right)=\frac{4}{5}x-20$$

Express \frac{3}{4}\left(-10\right) as a single fraction.

$$\frac{3}{4}x+\frac{3\left(-10\right)}{4}=\frac{4}{5}x-20$$

Multiply 3 and -10 to get -30.

$$\frac{3}{4}x+\frac{-30}{4}=\frac{4}{5}x-20$$

Reduce the fraction \frac{-30}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}x-\frac{15}{2}=\frac{4}{5}x-20$$

Subtract \frac{4}{5}x from both sides.

$$\frac{3}{4}x-\frac{15}{2}-\frac{4}{5}x=-20$$

Combine \frac{3}{4}x and -\frac{4}{5}x to get -\frac{1}{20}x.

$$-\frac{1}{20}x-\frac{15}{2}=-20$$

Add \frac{15}{2} to both sides.

$$-\frac{1}{20}x=-20+\frac{15}{2}$$

Convert -20 to fraction -\frac{40}{2}.

$$-\frac{1}{20}x=-\frac{40}{2}+\frac{15}{2}$$

Since -\frac{40}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$-\frac{1}{20}x=\frac{-40+15}{2}$$

Add -40 and 15 to get -25.

$$-\frac{1}{20}x=-\frac{25}{2}$$

Multiply both sides by -20, the reciprocal of -\frac{1}{20}.

$$x=-\frac{25}{2}\left(-20\right)$$

Express -\frac{25}{2}\left(-20\right) as a single fraction.

$$x=\frac{-25\left(-20\right)}{2}$$

Multiply -25 and -20 to get 500.

$$x=\frac{500}{2}$$

Divide 500 by 2 to get 250.

$$x=250$$