Solve the Inequality for x x-1/4<=-1/2

$x - \frac{1}{4} \leq - \frac{1}{2}$

Step 1

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

$x \leq - \frac{1}{2} + \frac{1}{4}$

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $2$ .

$x \leq - \frac{2}{4} + \frac{1}{4}$

Step 4

Combine the numerators over the common denominator.

$x \leq \frac{- 2 + 1}{4}$

Step 5

Add $- 2$ and $1$ .

$x \leq \frac{- 1}{4}$

Step 6

Move the negative in front of the fraction.

$x \leq - \frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{1}{4}$

Interval Notation:

$(- \infty, - \frac{1}{4}]$