Solve for x 13-3/2x=37

$13 - \frac{3}{2} x = 37$

Step 1

Simplify each term.

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

$13 - \frac{x \cdot 3}{2} = 37$

Move $3$ to the left of $x$ .

$13 - \frac{3 x}{2} = 37$

Step 2

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

Subtract $13$ from both sides of the equation.

$- \frac{3 x}{2} = 37 - 13$

Subtract $13$ from $37$ .

$- \frac{3 x}{2} = 24$

Step 3

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

$- \frac{2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot 24$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{3} (- \frac{3 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot 24$

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot 24$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot 24$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot 24$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{2}{3} \cdot 24$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot 24$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot 24$

Rewrite the expression.

$- - x = - \frac{2}{3} \cdot 24$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{3} \cdot 24$

Multiply $x$ by $1$ .

$x = - \frac{2}{3} \cdot 24$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot 24$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x = \frac{- 2}{3} \cdot 24$

Factor $3$ out of $24$ .

$x = \frac{- 2}{3} \cdot (3 (8))$

Cancel the common factor.

$x = \frac{- 2}{3} \cdot (3 \cdot 8)$

Rewrite the expression.

$x = - 2 \cdot 8$

Multiply $- 2$ by $8$ .

$x = - 16$

Solve for x 13-3/2x=37

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