Solve 2/3(t-2)=3/4(t+2)

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

Solve for t

$$t=-34$$

Steps for Solving Linear Equation

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

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

Express \frac{2}{3}\left(-2\right) as a single fraction.

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

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

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

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

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

Multiply 3 and 2 to get 6.

$$\frac{2}{3}t-\frac{4}{3}=\frac{3}{4}t+\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

$$\frac{2}{3}t-\frac{4}{3}-\frac{3}{4}t=\frac{3}{2}$$

Combine \frac{2}{3}t and -\frac{3}{4}t to get -\frac{1}{12}t.

$$-\frac{1}{12}t-\frac{4}{3}=\frac{3}{2}$$

Add \frac{4}{3} to both sides.

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

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$-\frac{1}{12}t=\frac{9}{6}+\frac{8}{6}$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{12}t=\frac{9+8}{6}$$

Add 9 and 8 to get 17.

$$-\frac{1}{12}t=\frac{17}{6}$$

Multiply both sides by -12, the reciprocal of -\frac{1}{12}.

$$t=\frac{17}{6}\left(-12\right)$$

Express \frac{17}{6}\left(-12\right) as a single fraction.

$$t=\frac{17\left(-12\right)}{6}$$

Multiply 17 and -12 to get -204.

$$t=\frac{-204}{6}$$

Divide -204 by 6 to get -34.

$$t=-34$$