Solve the Inequality for x 1/2x-1/4<5/8

$\frac{1}{2} x - \frac{1}{4} < \frac{5}{8}$

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - \frac{1}{4} < \frac{5}{8}$

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

Add $\frac{1}{4}$ to both sides of the inequality.

$\frac{x}{2} < \frac{5}{8} + \frac{1}{4}$

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

$\frac{x}{2} < \frac{5}{8} + \frac{1}{4} \cdot \frac{2}{2}$

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

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

$\frac{x}{2} < \frac{5}{8} + \frac{2}{4 \cdot 2}$

Multiply $4$ by $2$ .

$\frac{x}{2} < \frac{5}{8} + \frac{2}{8}$

Combine the numerators over the common denominator.

$\frac{x}{2} < \frac{5 + 2}{8}$

Add $5$ and $2$ .

$\frac{x}{2} < \frac{7}{8}$

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 < \frac{7}{8} \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 < \frac{7}{8} \cdot 2$

Rewrite the expression.

$x < \frac{7}{8} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$x < \frac{7}{2 (4)} \cdot 2$

Cancel the common factor.

$x < \frac{7}{2 \cdot 4} \cdot 2$

Rewrite the expression.

$x < \frac{7}{4}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{7}{4}$

Interval Notation:

$(- \infty, \frac{7}{4})$