Pre-Algebra Examples

$x + \frac{1}{3} + 1 = \frac{1}{4} + \frac{1}{8}$

Step 1

Simplify $x + \frac{1}{3} + 1$ .

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Step 1.1

Write $1$ as a fraction with a common denominator.

$x + \frac{1}{3} + \frac{3}{3} = \frac{1}{4} + \frac{1}{8}$

Step 1.2

Combine the numerators over the common denominator.

$x + \frac{1 + 3}{3} = \frac{1}{4} + \frac{1}{8}$

Step 1.3

Add $1$ and $3$ .

$x + \frac{4}{3} = \frac{1}{4} + \frac{1}{8}$

Step 2

Simplify $\frac{1}{4} + \frac{1}{8}$ .

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Step 2.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x + \frac{4}{3} = \frac{1}{4} \cdot \frac{2}{2} + \frac{1}{8}$

Step 2.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$x + \frac{4}{3} = \frac{2}{4 \cdot 2} + \frac{1}{8}$

Step 2.2.2

Multiply $4$ by $2$ .

$x + \frac{4}{3} = \frac{2}{8} + \frac{1}{8}$

Step 2.3

Combine the numerators over the common denominator.

$x + \frac{4}{3} = \frac{2 + 1}{8}$

Step 2.4

Add $2$ and $1$ .

$x + \frac{4}{3} = \frac{3}{8}$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 0.95833333$

Step 4