Solve 32/60=2x+6/52.5

$$\frac{ 32 }{ 60 } = \frac{ 2x+6 }{ 52.5 }$$

Solve for x

$$x=11$$

Steps for Solving Linear Equation

Reduce the fraction \frac{32}{60} to lowest terms by extracting and canceling out 4.

$$\frac{8}{15}=\frac{2x+6}{52.5}$$

Divide each term of 2x+6 by 52.5 to get \frac{2x}{52.5}+\frac{6}{52.5}.

$$\frac{8}{15}=\frac{2x}{52.5}+\frac{6}{52.5}$$

Divide 2x by 52.5 to get \frac{4}{105}x.

$$\frac{8}{15}=\frac{4}{105}x+\frac{6}{52.5}$$

Expand \frac{6}{52.5} by multiplying both numerator and the denominator by 10.

$$\frac{8}{15}=\frac{4}{105}x+\frac{60}{525}$$

Reduce the fraction \frac{60}{525} to lowest terms by extracting and canceling out 15.

$$\frac{8}{15}=\frac{4}{105}x+\frac{4}{35}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{4}{105}x+\frac{4}{35}=\frac{8}{15}$$

Subtract \frac{4}{35} from both sides.

$$\frac{4}{105}x=\frac{8}{15}-\frac{4}{35}$$

Least common multiple of 15 and 35 is 105. Convert \frac{8}{15} and \frac{4}{35} to fractions with denominator 105.

$$\frac{4}{105}x=\frac{56}{105}-\frac{12}{105}$$

Since \frac{56}{105} and \frac{12}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{105}x=\frac{56-12}{105}$$

Subtract 12 from 56 to get 44.

$$\frac{4}{105}x=\frac{44}{105}$$

Divide both sides by \frac{4}{105}.

$$x=\frac{\frac{44}{105}}{\frac{4}{105}}$$

Express \frac{\frac{44}{105}}{\frac{4}{105}} as a single fraction.

$$x=\frac{44}{105\times \frac{4}{105}}$$

Multiply 105 and \frac{4}{105} to get 4.

$$x=\frac{44}{4}$$

Divide 44 by 4 to get 11.

$$x=11$$