Solve for h 2/3h-3/2=-1/2h+2

$\frac{2}{3} h - \frac{3}{2} = - \frac{1}{2} h + 2$

Combine $\frac{2}{3}$ and $h$ .

$\frac{2 h}{3} - \frac{3}{2} = - \frac{1}{2} h + 2$

Combine $h$ and $\frac{1}{2}$ .

$\frac{2 h}{3} - \frac{3}{2} = - \frac{h}{2} + 2$

Move all terms containing $h$ to the left side of the equation.

Add $\frac{h}{2}$ to both sides of the equation.

$\frac{2 h}{3} - \frac{3}{2} + \frac{h}{2} = 2$

To write $\frac{2 h}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 h}{3} \cdot \frac{2}{2} + \frac{h}{2} - \frac{3}{2} = 2$

To write $\frac{h}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 h}{3} \cdot \frac{2}{2} + \frac{h}{2} \cdot \frac{3}{3} - \frac{3}{2} = 2$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 h}{3}$ by $\frac{2}{2}$ .

$\frac{2 h \cdot 2}{3 \cdot 2} + \frac{h}{2} \cdot \frac{3}{3} - \frac{3}{2} = 2$

Multiply $3$ by $2$ .

$\frac{2 h \cdot 2}{6} + \frac{h}{2} \cdot \frac{3}{3} - \frac{3}{2} = 2$

Multiply $\frac{h}{2}$ by $\frac{3}{3}$ .

$\frac{2 h \cdot 2}{6} + \frac{h \cdot 3}{2 \cdot 3} - \frac{3}{2} = 2$

Multiply $2$ by $3$ .

$\frac{2 h \cdot 2}{6} + \frac{h \cdot 3}{6} - \frac{3}{2} = 2$

Combine the numerators over the common denominator.

$\frac{2 h \cdot 2 + h \cdot 3}{6} - \frac{3}{2} = 2$

Simplify each term.

Simplify the numerator.

Factor $h$ out of $2 h \cdot 2 + h \cdot 3$ .

Factor $h$ out of $2 h \cdot 2$ .

$\frac{h (2 \cdot 2) + h \cdot 3}{6} - \frac{3}{2} = 2$

Factor $h$ out of $h \cdot 3$ .

$\frac{h (2 \cdot 2) + h (3)}{6} - \frac{3}{2} = 2$

Factor $h$ out of $h (2 \cdot 2) + h (3)$ .

$\frac{h (2 \cdot 2 + 3)}{6} - \frac{3}{2} = 2$

Multiply $2$ by $2$ .

$\frac{h (4 + 3)}{6} - \frac{3}{2} = 2$

Add $4$ and $3$ .

$\frac{h \cdot 7}{6} - \frac{3}{2} = 2$

Move $7$ to the left of $h$ .

$\frac{7 h}{6} - \frac{3}{2} = 2$

Move all terms not containing $h$ to the right side of the equation.

Add $\frac{3}{2}$ to both sides of the equation.

$\frac{7 h}{6} = 2 + \frac{3}{2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 h}{6} = 2 \cdot \frac{2}{2} + \frac{3}{2}$

Combine $2$ and $\frac{2}{2}$ .

$\frac{7 h}{6} = \frac{2 \cdot 2}{2} + \frac{3}{2}$

Combine the numerators over the common denominator.

$\frac{7 h}{6} = \frac{2 \cdot 2 + 3}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{7 h}{6} = \frac{4 + 3}{2}$

Add $4$ and $3$ .

$\frac{7 h}{6} = \frac{7}{2}$

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 h}{6} = \frac{6}{7} \cdot \frac{7}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{7} \cdot \frac{7 h}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 h}{6} = \frac{6}{7} \cdot \frac{7}{2}$

Rewrite the expression.

$\frac{1}{7} (7 h) = \frac{6}{7} \cdot \frac{7}{2}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 h$ .

$\frac{1}{7} (7 (h)) = \frac{6}{7} \cdot \frac{7}{2}$

Cancel the common factor.

$\frac{1}{7} (7 h) = \frac{6}{7} \cdot \frac{7}{2}$

Rewrite the expression.

$h = \frac{6}{7} \cdot \frac{7}{2}$

Simplify the right side.

Simplify $\frac{6}{7} \cdot \frac{7}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$h = \frac{2 (3)}{7} \cdot \frac{7}{2}$

Cancel the common factor.

$h = \frac{2 \cdot 3}{7} \cdot \frac{7}{2}$

Rewrite the expression.

$h = \frac{3}{7} \cdot 7$

Cancel the common factor of $7$ .

Cancel the common factor.

$h = \frac{3}{7} \cdot 7$

Rewrite the expression.

$h = 3$

Solve for h 2/3h-3/2=-1/2h+2

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