Solve 0.75(x+51/2)=5/8

$$0.75 ( x + 51 / 2 ) = \frac { 5 } { 8 }$$

Solve for x

$$x = -\frac{74}{3} = -24\frac{2}{3} \approx -24.666666667$$

Steps for Solving Linear Equation

Divide both sides by 0.75.

$$x+\frac{51}{2}=\frac{\frac{5}{8}}{0.75}$$

Express \frac{\frac{5}{8}}{0.75} as a single fraction.

$$x+\frac{51}{2}=\frac{5}{8\times 0.75}$$

Multiply 8 and 0.75 to get 6.

$$x+\frac{51}{2}=\frac{5}{6}$$

Subtract \frac{51}{2} from both sides.

$$x=\frac{5}{6}-\frac{51}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{51}{2} to fractions with denominator 6.

$$x=\frac{5}{6}-\frac{153}{6}$$

Since \frac{5}{6} and \frac{153}{6} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{5-153}{6}$$

Subtract 153 from 5 to get -148.

$$x=\frac{-148}{6}$$

Reduce the fraction \frac{-148}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{74}{3}$$