Solve 3/2(3/2x-6)=9/2

$$\frac { 3 } { 2 } ( \frac { 3 } { 2 } x - 6 ) = \frac { 9 } { 2 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$\frac{3}{2}x-6=\frac{9}{2}\times \frac{2}{3}$$

Multiply \frac{9}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}x-6=\frac{9\times 2}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{2}x-6=\frac{9}{3}$$

Divide 9 by 3 to get 3.

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

Add 6 to both sides.

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

Add 3 and 6 to get 9.

$$\frac{3}{2}x=9$$

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

$$x=9\times \frac{2}{3}$$

Express 9\times \frac{2}{3} as a single fraction.

$$x=\frac{9\times 2}{3}$$

Multiply 9 and 2 to get 18.

$$x=\frac{18}{3}$$

Divide 18 by 3 to get 6.

$$x=6$$