Solve y=1/2x(3/2)^2-3/2+3/2-2

$$y = \frac { 1 } { 2 } x ( \frac { 3 } { 2 } ) ^ { 2 } - \frac { 3 } { 2 } + \frac { 3 } { 2 } - 2$$

Solve for x

$$x=\frac{8\left(y+2\right)}{9}$$

Steps for Solving Linear Equation

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$y=\frac{1}{2}x\times \frac{9}{4}-\frac{3}{2}+\frac{3}{2}-2$$

Multiply \frac{1}{2} and \frac{9}{4} to get \frac{9}{8}.

$$y=\frac{9}{8}x-\frac{3}{2}+\frac{3}{2}-2$$

Add -\frac{3}{2} and \frac{3}{2} to get 0.

$$y=\frac{9}{8}x-2$$

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

$$\frac{9}{8}x-2=y$$

Add 2 to both sides.

$$\frac{9}{8}x=y+2$$

Divide both sides of the equation by \frac{9}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{9}{8}x}{\frac{9}{8}}=\frac{y+2}{\frac{9}{8}}$$

Dividing by \frac{9}{8} undoes the multiplication by \frac{9}{8}.

$$x=\frac{y+2}{\frac{9}{8}}$$

Divide y+2 by \frac{9}{8} by multiplying y+2 by the reciprocal of \frac{9}{8}.

$$x=\frac{8y+16}{9}$$

Solve for y

$$y=\frac{9x}{8}-2$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$y=\frac{1}{2}x\times \frac{9}{4}-\frac{3}{2}+\frac{3}{2}-2$$

Multiply \frac{1}{2} and \frac{9}{4} to get \frac{9}{8}.

$$y=\frac{9}{8}x-\frac{3}{2}+\frac{3}{2}-2$$

Add -\frac{3}{2} and \frac{3}{2} to get 0.

$$y=\frac{9}{8}x-2$$