Basic Math Examples

$\frac{3}{2} + \frac{3}{4} a = \frac{1}{4} a - \frac{1}{2}$

Step 1

Combine $\frac{3}{4}$ and $a$ .

$\frac{3}{2} + \frac{3 a}{4} = \frac{1}{4} a - \frac{1}{2}$

Step 2

Combine $\frac{1}{4}$ and $a$ .

$\frac{3}{2} + \frac{3 a}{4} = \frac{a}{4} - \frac{1}{2}$

Step 3

Move all terms containing $a$ to the left side of the equation.

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Step 3.1

Subtract $\frac{a}{4}$ from both sides of the equation.

$\frac{3}{2} + \frac{3 a}{4} - \frac{a}{4} = - \frac{1}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3}{2} + \frac{3 a - a}{4} = - \frac{1}{2}$

Step 3.3

Subtract $a$ from $3 a$ .

$\frac{3}{2} + \frac{2 a}{4} = - \frac{1}{2}$

Step 3.4

Cancel the common factor of $2$ and $4$ .

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Step 3.4.1

Factor $2$ out of $2 a$ .

$\frac{3}{2} + \frac{2 (a)}{4} = - \frac{1}{2}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $4$ .

$\frac{3}{2} + \frac{2 a}{2 \cdot 2} = - \frac{1}{2}$

Step 3.4.2.2

Cancel the common factor.

$\frac{3}{2} + \frac{2 a}{2 \cdot 2} = - \frac{1}{2}$

Step 3.4.2.3

Rewrite the expression.

$\frac{3}{2} + \frac{a}{2} = - \frac{1}{2}$

Step 4

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

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Step 4.1

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{a}{2} = - \frac{1}{2} - \frac{3}{2}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{a}{2} = \frac{- 1 - 3}{2}$

Step 4.3

Subtract $3$ from $- 1$ .

$\frac{a}{2} = \frac{- 4}{2}$

Step 4.4

Divide $- 4$ by $2$ .

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

Step 5

Multiply both sides of the equation by $2$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

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

Step 6.1.1.2

Rewrite the expression.

$a = 2 \cdot - 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $2$ by $- 2$ .

$a = - 4$