Pre-Algebra Examples

$\frac{1}{4} + x < \frac{5}{6}$

Step 1

Subtract $\frac{1}{4}$ from both sides of the inequality.

$x < \frac{5}{6} - \frac{1}{4}$

Step 2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x < \frac{5}{6} \cdot \frac{2}{2} - \frac{1}{4}$

Step 3

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x < \frac{5}{6} \cdot \frac{2}{2} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$x < \frac{5 \cdot 2}{6 \cdot 2} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4.2

Multiply $6$ by $2$ .

$x < \frac{5 \cdot 2}{12} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$x < \frac{5 \cdot 2}{12} - \frac{3}{4 \cdot 3}$

Step 4.4

Multiply $4$ by $3$ .

$x < \frac{5 \cdot 2}{12} - \frac{3}{12}$

Step 5

Combine the numerators over the common denominator.

$x < \frac{5 \cdot 2 - 3}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $2$ .

$x < \frac{10 - 3}{12}$

Step 6.2

Subtract $3$ from $10$ .

$x < \frac{7}{12}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{7}{12}$

Interval Notation:

$(- \infty, \frac{7}{12})$