\[ \frac{1}{2}-\frac{1}{4} x \geq-\frac{1}{4} \] Apply properties: \( \square \) Add Subtract Multiply Divide To start over: Reset

To solve the inequality \(\frac{1}{2} - \frac{1}{4} x \geq -\frac{1}{4}\), first, let's isolate the term with \(x\). Start by adding \(\frac{1}{4}\) to both sides: \[ \frac{1}{2} + \frac{1}{4} \geq -\frac{1}{4} + \frac{1}{4} \] This simplifies to \(\frac{1}{2} + \frac{1}{4} \geq 0\). Next, convert \(\frac{1}{2}\) to fourths: \(\frac{1}{2} = \frac{2}{4}\), so we have: \[ \frac{2}{4} + \frac{1}{4} \geq 0 \] \[ \frac{3}{4} \geq 0 \] Now, this tells us that the left side of the inequality is always positive. Now we need to isolate \(x\): Subtract \(\frac{1}{2}\) from both sides: \[ -\frac{1}{4} x \geq -\frac{1}{4} - \frac{1}{2} \] Convert \(-\frac{1}{2}\) to fourths: \(-\frac{1}{2} = -\frac{2}{4}\): \[ -\frac{1}{4} x \geq -\frac{1}{4} - \frac{2}{4} \] \[ -\frac{1}{4} x \geq -\frac{3}{4} \] Finally, multiply both sides by \(-4\) (remember to flip the inequality sign): \[ x \leq 3 \] So, the solution to the inequality is: \[ x \leq 3 \] Now you know how to tackle inequalities step by step!