Solve for n 3/2n-8/3=-29/12

$\frac{3}{2} n - \frac{8}{3} = - \frac{29}{12}$

Step 1

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

$\frac{3 n}{2} - \frac{8}{3} = - \frac{29}{12}$

Step 2

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

Add $\frac{8}{3}$ to both sides of the equation.

$\frac{3 n}{2} = - \frac{29}{12} + \frac{8}{3}$

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 n}{2} = - \frac{29}{12} + \frac{8}{3} \cdot \frac{4}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{3}$ by $\frac{4}{4}$ .

$\frac{3 n}{2} = - \frac{29}{12} + \frac{8 \cdot 4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$\frac{3 n}{2} = - \frac{29}{12} + \frac{8 \cdot 4}{12}$

Combine the numerators over the common denominator.

$\frac{3 n}{2} = \frac{- 29 + 8 \cdot 4}{12}$

Simplify the numerator.

Multiply $8$ by $4$ .

$\frac{3 n}{2} = \frac{- 29 + 32}{12}$

Add $- 29$ and $32$ .

$\frac{3 n}{2} = \frac{3}{12}$

Cancel the common factor of $3$ and $12$ .

Factor $3$ out of $3$ .

$\frac{3 n}{2} = \frac{3 (1)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$\frac{3 n}{2} = \frac{3 \cdot 1}{3 \cdot 4}$

Cancel the common factor.

$\frac{3 n}{2} = \frac{3 \cdot 1}{3 \cdot 4}$

Rewrite the expression.

$\frac{3 n}{2} = \frac{1}{4}$

Step 3

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

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} \cdot \frac{1}{4}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 n}{2} = \frac{2}{3} \cdot \frac{1}{4}$

Rewrite the expression.

$\frac{1}{3} (3 n) = \frac{2}{3} \cdot \frac{1}{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 n$ .

$\frac{1}{3} (3 (n)) = \frac{2}{3} \cdot \frac{1}{4}$

Cancel the common factor.

$\frac{1}{3} (3 n) = \frac{2}{3} \cdot \frac{1}{4}$

Rewrite the expression.

$n = \frac{2}{3} \cdot \frac{1}{4}$

Simplify the right side.

Simplify $\frac{2}{3} \cdot \frac{1}{4}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$n = \frac{2}{3} \cdot \frac{1}{2 (2)}$

Cancel the common factor.

$n = \frac{2}{3} \cdot \frac{1}{2 \cdot 2}$

Rewrite the expression.

$n = \frac{1}{3} \cdot \frac{1}{2}$

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$n = \frac{1}{3 \cdot 2}$

Multiply $3$ by $2$ .

$n = \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{6}$

Decimal Form:

$n = 0.1\overline{6}$

Solve for n 3/2n-8/3=-29/12

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