Basic Math Examples

$\frac{3}{2} a + \frac{5}{2} = - \frac{7}{2}$

Step 1

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

$\frac{3 a}{2} + \frac{5}{2} = - \frac{7}{2}$

Step 2

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

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Step 2.1

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

$\frac{3 a}{2} = - \frac{7}{2} - \frac{5}{2}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 a}{2} = \frac{- 7 - 5}{2}$

Step 2.3

Subtract $5$ from $- 7$ .

$\frac{3 a}{2} = \frac{- 12}{2}$

Step 2.4

Divide $- 12$ by $2$ .

$\frac{3 a}{2} = - 6$

Step 3

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

$\frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot - 6$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 a}{2} = \frac{2}{3} \cdot - 6$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 a) = \frac{2}{3} \cdot - 6$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 a$ .

$\frac{1}{3} (3 (a)) = \frac{2}{3} \cdot - 6$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 a) = \frac{2}{3} \cdot - 6$

Step 4.1.1.2.3

Rewrite the expression.

$a = \frac{2}{3} \cdot - 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{3} \cdot - 6$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $- 6$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$a = 2 \cdot - 2$

Step 4.2.1.2

Multiply $2$ by $- 2$ .

$a = - 4$