Solve for p 3/2p-2=-7/8

$\frac{3}{2} p - 2 = - \frac{7}{8}$

Step 1

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

$\frac{3 p}{2} - 2 = - \frac{7}{8}$

Step 2

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

Add $2$ to both sides of the equation.

$\frac{3 p}{2} = - \frac{7}{8} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3 p}{2} = - \frac{7}{8} + 2 \cdot \frac{8}{8}$

Combine $2$ and $\frac{8}{8}$ .

$\frac{3 p}{2} = - \frac{7}{8} + \frac{2 \cdot 8}{8}$

Combine the numerators over the common denominator.

$\frac{3 p}{2} = \frac{- 7 + 2 \cdot 8}{8}$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{3 p}{2} = \frac{- 7 + 16}{8}$

Add $- 7$ and $16$ .

$\frac{3 p}{2} = \frac{9}{8}$

Step 3

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 p}{2} = \frac{2}{3} \cdot \frac{9}{8}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 p}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 p}{2} = \frac{2}{3} \cdot \frac{9}{8}$

Rewrite the expression.

$\frac{1}{3} (3 p) = \frac{2}{3} \cdot \frac{9}{8}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 p$ .

$\frac{1}{3} (3 (p)) = \frac{2}{3} \cdot \frac{9}{8}$

Cancel the common factor.

$\frac{1}{3} (3 p) = \frac{2}{3} \cdot \frac{9}{8}$

Rewrite the expression.

$p = \frac{2}{3} \cdot \frac{9}{8}$

Simplify the right side.

Simplify $\frac{2}{3} \cdot \frac{9}{8}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$p = \frac{2}{3} \cdot \frac{9}{2 (4)}$

Cancel the common factor.

$p = \frac{2}{3} \cdot \frac{9}{2 \cdot 4}$

Rewrite the expression.

$p = \frac{1}{3} \cdot \frac{9}{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$p = \frac{1}{3} \cdot \frac{3 (3)}{4}$

Cancel the common factor.

$p = \frac{1}{3} \cdot \frac{3 \cdot 3}{4}$

Rewrite the expression.

$p = \frac{3}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{3}{4}$

Decimal Form:

$p = 0.75$

Solve for p 3/2p-2=-7/8

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