Solve 2/3(w-5)=3/4(w+2)

$$\frac { 2 } { 3 } ( w - 5 ) = \frac { 3 } { 4 } ( w + 2 )$$

Solve for w

$$w=-58$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}w+\frac{2}{3}\left(-5\right)=\frac{3}{4}\left(w+2\right)$$

Express \frac{2}{3}\left(-5\right) as a single fraction.

$$\frac{2}{3}w+\frac{2\left(-5\right)}{3}=\frac{3}{4}\left(w+2\right)$$

Multiply 2 and -5 to get -10.

$$\frac{2}{3}w+\frac{-10}{3}=\frac{3}{4}\left(w+2\right)$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{2}{3}w-\frac{10}{3}=\frac{3}{4}\left(w+2\right)$$

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

$$\frac{2}{3}w-\frac{10}{3}=\frac{3}{4}w+\frac{3}{4}\times 2$$

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

$$\frac{2}{3}w-\frac{10}{3}=\frac{3}{4}w+\frac{3\times 2}{4}$$

Multiply 3 and 2 to get 6.

$$\frac{2}{3}w-\frac{10}{3}=\frac{3}{4}w+\frac{6}{4}$$

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

$$\frac{2}{3}w-\frac{10}{3}=\frac{3}{4}w+\frac{3}{2}$$

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

$$\frac{2}{3}w-\frac{10}{3}-\frac{3}{4}w=\frac{3}{2}$$

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

$$-\frac{1}{12}w-\frac{10}{3}=\frac{3}{2}$$

Add \frac{10}{3} to both sides.

$$-\frac{1}{12}w=\frac{3}{2}+\frac{10}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{10}{3} to fractions with denominator 6.

$$-\frac{1}{12}w=\frac{9}{6}+\frac{20}{6}$$

Since \frac{9}{6} and \frac{20}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{12}w=\frac{9+20}{6}$$

Add 9 and 20 to get 29.

$$-\frac{1}{12}w=\frac{29}{6}$$

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

$$w=\frac{29}{6}\left(-12\right)$$

Express \frac{29}{6}\left(-12\right) as a single fraction.

$$w=\frac{29\left(-12\right)}{6}$$

Multiply 29 and -12 to get -348.

$$w=\frac{-348}{6}$$

Divide -348 by 6 to get -58.

$$w=-58$$