Solve 9/2(2a+40)=75

$$\frac { 9 } { 2 } ( 2 a + 40 ) = 75$$

Solve for a

$$a = -\frac{35}{3} = -11\frac{2}{3} \approx -11.666666667$$

Steps for Solving Linear Equation

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$2a+40=75\times \frac{2}{9}$$

Express 75\times \frac{2}{9} as a single fraction.

$$2a+40=\frac{75\times 2}{9}$$

Multiply 75 and 2 to get 150.

$$2a+40=\frac{150}{9}$$

Reduce the fraction \frac{150}{9} to lowest terms by extracting and canceling out 3.

$$2a+40=\frac{50}{3}$$

Subtract 40 from both sides.

$$2a=\frac{50}{3}-40$$

Convert 40 to fraction \frac{120}{3}.

$$2a=\frac{50}{3}-\frac{120}{3}$$

Since \frac{50}{3} and \frac{120}{3} have the same denominator, subtract them by subtracting their numerators.

$$2a=\frac{50-120}{3}$$

Subtract 120 from 50 to get -70.

$$2a=-\frac{70}{3}$$

Divide both sides by 2.

$$a=\frac{-\frac{70}{3}}{2}$$

Express \frac{-\frac{70}{3}}{2} as a single fraction.

$$a=\frac{-70}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$a=\frac{-70}{6}$$

Reduce the fraction \frac{-70}{6} to lowest terms by extracting and canceling out 2.

$$a=-\frac{35}{3}$$