Solve 3/5(v+2)=1/2(v-3)

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

Solve for v

$$v=-27$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{5} by v+2.

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

Express \frac{3}{5}\times 2 as a single fraction.

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

Multiply 3 and 2 to get 6.

$$\frac{3}{5}v+\frac{6}{5}=\frac{1}{2}\left(v-3\right)$$

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

$$\frac{3}{5}v+\frac{6}{5}=\frac{1}{2}v+\frac{1}{2}\left(-3\right)$$

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

$$\frac{3}{5}v+\frac{6}{5}=\frac{1}{2}v+\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{3}{5}v+\frac{6}{5}=\frac{1}{2}v-\frac{3}{2}$$

Subtract \frac{1}{2}v from both sides.

$$\frac{3}{5}v+\frac{6}{5}-\frac{1}{2}v=-\frac{3}{2}$$

Combine \frac{3}{5}v and -\frac{1}{2}v to get \frac{1}{10}v.

$$\frac{1}{10}v+\frac{6}{5}=-\frac{3}{2}$$

Subtract \frac{6}{5} from both sides.

$$\frac{1}{10}v=-\frac{3}{2}-\frac{6}{5}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{3}{2} and \frac{6}{5} to fractions with denominator 10.

$$\frac{1}{10}v=-\frac{15}{10}-\frac{12}{10}$$

Since -\frac{15}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{10}v=\frac{-15-12}{10}$$

Subtract 12 from -15 to get -27.

$$\frac{1}{10}v=-\frac{27}{10}$$

Multiply both sides by 10, the reciprocal of \frac{1}{10}.

$$v=-\frac{27}{10}\times 10$$

Cancel out 10 and 10.

$$v=-27$$