Solve 1/2x+8/6(x+20)=34

$$\frac { 1 } { 2 } x + \frac { 8 } { 6 } ( x + 20 ) = 34$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+\frac{4}{3}\left(x+20\right)=34$$

Use the distributive property to multiply \frac{4}{3} by x+20.

$$\frac{1}{2}x+\frac{4}{3}x+\frac{4}{3}\times 20=34$$

Express \frac{4}{3}\times 20 as a single fraction.

$$\frac{1}{2}x+\frac{4}{3}x+\frac{4\times 20}{3}=34$$

Multiply 4 and 20 to get 80.

$$\frac{1}{2}x+\frac{4}{3}x+\frac{80}{3}=34$$

Combine \frac{1}{2}x and \frac{4}{3}x to get \frac{11}{6}x.

$$\frac{11}{6}x+\frac{80}{3}=34$$

Subtract \frac{80}{3} from both sides.

$$\frac{11}{6}x=34-\frac{80}{3}$$

Convert 34 to fraction \frac{102}{3}.

$$\frac{11}{6}x=\frac{102}{3}-\frac{80}{3}$$

Since \frac{102}{3} and \frac{80}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{6}x=\frac{102-80}{3}$$

Subtract 80 from 102 to get 22.

$$\frac{11}{6}x=\frac{22}{3}$$

Multiply both sides by \frac{6}{11}, the reciprocal of \frac{11}{6}.

$$x=\frac{22}{3}\times \frac{6}{11}$$

Multiply \frac{22}{3} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{22\times 6}{3\times 11}$$

Do the multiplications in the fraction \frac{22\times 6}{3\times 11}.

$$x=\frac{132}{33}$$

Divide 132 by 33 to get 4.

$$x=4$$