Solve 5/4(2x+4)=x+19

$$\frac { 5 } { 4 } ( 2 x + 4 ) = x + 19$$

Solve for x

$$x = \frac{28}{3} = 9\frac{1}{3} \approx 9.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{4} by 2x+4.

$$\frac{5}{4}\times 2x+\frac{5}{4}\times 4=x+19$$

Express \frac{5}{4}\times 2 as a single fraction.

$$\frac{5\times 2}{4}x+\frac{5}{4}\times 4=x+19$$

Multiply 5 and 2 to get 10.

$$\frac{10}{4}x+\frac{5}{4}\times 4=x+19$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}x+\frac{5}{4}\times 4=x+19$$

Cancel out 4 and 4.

$$\frac{5}{2}x+5=x+19$$

Subtract x from both sides.

$$\frac{5}{2}x+5-x=19$$

Combine \frac{5}{2}x and -x to get \frac{3}{2}x.

$$\frac{3}{2}x+5=19$$

Subtract 5 from both sides.

$$\frac{3}{2}x=19-5$$

Subtract 5 from 19 to get 14.

$$\frac{3}{2}x=14$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$x=14\times \frac{2}{3}$$

Express 14\times \frac{2}{3} as a single fraction.

$$x=\frac{14\times 2}{3}$$

Multiply 14 and 2 to get 28.

$$x=\frac{28}{3}$$