Solve 9t-3/4(5t-1)=5t+5/8

$$9 t - \frac { 3 } { 4 } ( 5 t - 1 ) = 5 t + \frac { 5 } { 8 }$$

Solve for t

$$t=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{3}{4} by 5t-1.

$$9t-\frac{3}{4}\times 5t-\frac{3}{4}\left(-1\right)=5t+\frac{5}{8}$$

Express -\frac{3}{4}\times 5 as a single fraction.

$$9t+\frac{-3\times 5}{4}t-\frac{3}{4}\left(-1\right)=5t+\frac{5}{8}$$

Multiply -3 and 5 to get -15.

$$9t+\frac{-15}{4}t-\frac{3}{4}\left(-1\right)=5t+\frac{5}{8}$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$9t-\frac{15}{4}t-\frac{3}{4}\left(-1\right)=5t+\frac{5}{8}$$

Multiply -\frac{3}{4} and -1 to get \frac{3}{4}.

$$9t-\frac{15}{4}t+\frac{3}{4}=5t+\frac{5}{8}$$

Combine 9t and -\frac{15}{4}t to get \frac{21}{4}t.

$$\frac{21}{4}t+\frac{3}{4}=5t+\frac{5}{8}$$

Subtract 5t from both sides.

$$\frac{21}{4}t+\frac{3}{4}-5t=\frac{5}{8}$$

Combine \frac{21}{4}t and -5t to get \frac{1}{4}t.

$$\frac{1}{4}t+\frac{3}{4}=\frac{5}{8}$$

Subtract \frac{3}{4} from both sides.

$$\frac{1}{4}t=\frac{5}{8}-\frac{3}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{1}{4}t=\frac{5}{8}-\frac{6}{8}$$

Since \frac{5}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}t=\frac{5-6}{8}$$

Subtract 6 from 5 to get -1.

$$\frac{1}{4}t=-\frac{1}{8}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$t=-\frac{1}{8}\times 4$$

Express -\frac{1}{8}\times 4 as a single fraction.

$$t=\frac{-4}{8}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$t=-\frac{1}{2}$$