Solve 2/7(t+2/3)=1/5(t-2/3)

$$\frac { 2 } { 7 } ( t + \frac { 2 } { 3 } ) = \frac { 1 } { 5 } ( t - \frac { 2 } { 3 } )$$

Solve for t

$$t = -\frac{34}{9} = -3\frac{7}{9} \approx -3.777777778$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{7} by t+\frac{2}{3}.

$$\frac{2}{7}t+\frac{2}{7}\times \frac{2}{3}=\frac{1}{5}\left(t-\frac{2}{3}\right)$$

Multiply \frac{2}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}t+\frac{2\times 2}{7\times 3}=\frac{1}{5}\left(t-\frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{2\times 2}{7\times 3}.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}\left(t-\frac{2}{3}\right)$$

Use the distributive property to multiply \frac{1}{5} by t-\frac{2}{3}.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t+\frac{1}{5}\left(-\frac{2}{3}\right)$$

Multiply \frac{1}{5} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t+\frac{1\left(-2\right)}{5\times 3}$$

Do the multiplications in the fraction \frac{1\left(-2\right)}{5\times 3}.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t+\frac{-2}{15}$$

Fraction \frac{-2}{15} can be rewritten as -\frac{2}{15} by extracting the negative sign.

$$\frac{2}{7}t+\frac{4}{21}=\frac{1}{5}t-\frac{2}{15}$$

Subtract \frac{1}{5}t from both sides.

$$\frac{2}{7}t+\frac{4}{21}-\frac{1}{5}t=-\frac{2}{15}$$

Combine \frac{2}{7}t and -\frac{1}{5}t to get \frac{3}{35}t.

$$\frac{3}{35}t+\frac{4}{21}=-\frac{2}{15}$$

Subtract \frac{4}{21} from both sides.

$$\frac{3}{35}t=-\frac{2}{15}-\frac{4}{21}$$

Least common multiple of 15 and 21 is 105. Convert -\frac{2}{15} and \frac{4}{21} to fractions with denominator 105.

$$\frac{3}{35}t=-\frac{14}{105}-\frac{20}{105}$$

Since -\frac{14}{105} and \frac{20}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{35}t=\frac{-14-20}{105}$$

Subtract 20 from -14 to get -34.

$$\frac{3}{35}t=-\frac{34}{105}$$

Multiply both sides by \frac{35}{3}, the reciprocal of \frac{3}{35}.

$$t=-\frac{34}{105}\times \frac{35}{3}$$

Multiply -\frac{34}{105} times \frac{35}{3} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{-34\times 35}{105\times 3}$$

Do the multiplications in the fraction \frac{-34\times 35}{105\times 3}.

$$t=\frac{-1190}{315}$$

Reduce the fraction \frac{-1190}{315} to lowest terms by extracting and canceling out 35.

$$t=-\frac{34}{9}$$