Solve 1/8(x+0.5)=75%

$$\frac { 1 } { 8 } ( x + 0.5 ) = 75 \%$$

Solve for x

$$x=5.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{8} by x+0.5.

$$\frac{1}{8}x+\frac{1}{8}\times 0.5=\frac{75}{100}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}x+\frac{1}{8}\times \frac{1}{2}=\frac{75}{100}$$

Multiply \frac{1}{8} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{8}x+\frac{1\times 1}{8\times 2}=\frac{75}{100}$$

Do the multiplications in the fraction \frac{1\times 1}{8\times 2}.

$$\frac{1}{8}x+\frac{1}{16}=\frac{75}{100}$$

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{8}x+\frac{1}{16}=\frac{3}{4}$$

Subtract \frac{1}{16} from both sides.

$$\frac{1}{8}x=\frac{3}{4}-\frac{1}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{3}{4} and \frac{1}{16} to fractions with denominator 16.

$$\frac{1}{8}x=\frac{12}{16}-\frac{1}{16}$$

Since \frac{12}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{8}x=\frac{12-1}{16}$$

Subtract 1 from 12 to get 11.

$$\frac{1}{8}x=\frac{11}{16}$$

Multiply both sides by 8, the reciprocal of \frac{1}{8}.

$$x=\frac{11}{16}\times 8$$

Express \frac{11}{16}\times 8 as a single fraction.

$$x=\frac{11\times 8}{16}$$

Multiply 11 and 8 to get 88.

$$x=\frac{88}{16}$$

Reduce the fraction \frac{88}{16} to lowest terms by extracting and canceling out 8.

$$x=\frac{11}{2}$$