Algebra Examples

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

Step 1

Simplify $\frac{1}{4} + \frac{1}{2} + x$ .

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Step 1.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

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

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

Step 1.2.2

Multiply $2$ by $2$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Add $1$ and $2$ .

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

Step 2

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

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Step 2.1

Subtract $\frac{3}{4}$ from both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $3$ from $- 3$ .

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

Step 2.4

Cancel the common factor of $- 6$ and $4$ .

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Step 2.4.1

Factor $2$ out of $- 6$ .

$x = \frac{2 (- 3)}{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

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

Step 2.4.2.2

Cancel the common factor.

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

Step 2.4.2.3

Rewrite the expression.

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

Step 2.5

Move the negative in front of the fraction.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$