Solve 2/3(1/8+4t)-3/8=5/8

$$\frac { 2 } { 3 } ( \frac { 1 } { 8 } + 4 t ) - \frac { 3 } { 8 } = \frac { 5 } { 8 }$$

Solve for t

$$t=\frac{11}{32}=0.34375$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by \frac{1}{8}+4t.

$$\frac{2}{3}\times \frac{1}{8}+\frac{2}{3}\times 4t-\frac{3}{8}=\frac{5}{8}$$

Multiply \frac{2}{3} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{3\times 8}+\frac{2}{3}\times 4t-\frac{3}{8}=\frac{5}{8}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 8}.

$$\frac{2}{24}+\frac{2}{3}\times 4t-\frac{3}{8}=\frac{5}{8}$$

Reduce the fraction \frac{2}{24} to lowest terms by extracting and canceling out 2.

$$\frac{1}{12}+\frac{2}{3}\times 4t-\frac{3}{8}=\frac{5}{8}$$

Express \frac{2}{3}\times 4 as a single fraction.

$$\frac{1}{12}+\frac{2\times 4}{3}t-\frac{3}{8}=\frac{5}{8}$$

Multiply 2 and 4 to get 8.

$$\frac{1}{12}+\frac{8}{3}t-\frac{3}{8}=\frac{5}{8}$$

Least common multiple of 12 and 8 is 24. Convert \frac{1}{12} and \frac{3}{8} to fractions with denominator 24.

$$\frac{2}{24}+\frac{8}{3}t-\frac{9}{24}=\frac{5}{8}$$

Since \frac{2}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-9}{24}+\frac{8}{3}t=\frac{5}{8}$$

Subtract 9 from 2 to get -7.

$$-\frac{7}{24}+\frac{8}{3}t=\frac{5}{8}$$

Add \frac{7}{24} to both sides.

$$\frac{8}{3}t=\frac{5}{8}+\frac{7}{24}$$

Least common multiple of 8 and 24 is 24. Convert \frac{5}{8} and \frac{7}{24} to fractions with denominator 24.

$$\frac{8}{3}t=\frac{15}{24}+\frac{7}{24}$$

Since \frac{15}{24} and \frac{7}{24} have the same denominator, add them by adding their numerators.

$$\frac{8}{3}t=\frac{15+7}{24}$$

Add 15 and 7 to get 22.

$$\frac{8}{3}t=\frac{22}{24}$$

Reduce the fraction \frac{22}{24} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}t=\frac{11}{12}$$

Multiply both sides by \frac{3}{8}, the reciprocal of \frac{8}{3}.

$$t=\frac{11}{12}\times \frac{3}{8}$$

Multiply \frac{11}{12} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{11\times 3}{12\times 8}$$

Do the multiplications in the fraction \frac{11\times 3}{12\times 8}.

$$t=\frac{33}{96}$$

Reduce the fraction \frac{33}{96} to lowest terms by extracting and canceling out 3.

$$t=\frac{11}{32}$$