Solve 3/5(10)=2/3q-1/4(-12)

$$\frac { 3 } { 5 } ( 10 ) = \frac { 2 } { 3 } q - \frac { 1 } { 4 } ( - 12 )$$

Solve for q

$$q = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Express \frac{3}{5}\times 10 as a single fraction.

$$\frac{3\times 10}{5}=\frac{2}{3}q-\frac{1}{4}\left(-12\right)$$

Multiply 3 and 10 to get 30.

$$\frac{30}{5}=\frac{2}{3}q-\frac{1}{4}\left(-12\right)$$

Divide 30 by 5 to get 6.

$$6=\frac{2}{3}q-\frac{1}{4}\left(-12\right)$$

Multiply \frac{1}{4} and -12 to get \frac{-12}{4}.

$$6=\frac{2}{3}q-\frac{-12}{4}$$

Divide -12 by 4 to get -3.

$$6=\frac{2}{3}q-\left(-3\right)$$

The opposite of -3 is 3.

$$6=\frac{2}{3}q+3$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2}{3}q+3=6$$

Subtract 3 from both sides.

$$\frac{2}{3}q=6-3$$

Subtract 3 from 6 to get 3.

$$\frac{2}{3}q=3$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$q=3\times \frac{3}{2}$$

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

$$q=\frac{3\times 3}{2}$$

Multiply 3 and 3 to get 9.

$$q=\frac{9}{2}$$