Solve for x (9x)/4+5/2=-1/2

$\frac{9 x}{4} + \frac{5}{2} = - \frac{1}{2}$

Step 1

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

Subtract $\frac{5}{2}$ from both sides of the equation.

$\frac{9 x}{4} = - \frac{1}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$\frac{9 x}{4} = \frac{- 1 - 5}{2}$

Subtract $5$ from $- 1$ .

$\frac{9 x}{4} = \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$\frac{9 x}{4} = - 3$

Step 2

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} \cdot \frac{9 x}{4} = \frac{4}{9} \cdot - 3$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{9} \cdot \frac{9 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 x}{4} = \frac{4}{9} \cdot - 3$

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{4}{9} \cdot - 3$

Cancel the common factor of $9$ .

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{4}{9} \cdot - 3$

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{4}{9} \cdot - 3$

Rewrite the expression.

$x = \frac{4}{9} \cdot - 3$

Simplify the right side.

Simplify $\frac{4}{9} \cdot - 3$ .

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$x = \frac{4}{3 (3)} \cdot - 3$

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{4}{3} \cdot - 1$

Combine $\frac{4}{3}$ and $- 1$ .

$x = \frac{4 \cdot - 1}{3}$

Simplify the expression.

Multiply $4$ by $- 1$ .

$x = \frac{- 4}{3}$

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$

Solve for x (9x)/4+5/2=-1/2

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