Question

What is the solution to the given inequality? 1/2-1/4x>-1/4

Answer 1

Answer:

x ≤ 3

Step-by-step explanation:

$\dfrac{1}{2}-\dfrac{1}{4}x \geq -\dfrac{1}{4}$

Subtract 1/2 from both sides:

$\implies \dfrac{1}{2}-\dfrac{1}{4}x-\dfrac{1}{2} \geq -\dfrac{1}{4}-\dfrac{1}{2}$

$\implies -\dfrac{1}{4}x \geq -\dfrac{3}{4}$

Multiply both sides by 4:

$\implies -\dfrac{1}{4}x \cdot 4 \geq -\dfrac{3}{4} \cdot 4$

$\implies -x \geq -3$

Divide both sides by -1 (remembering to flip the sign):

$\implies \dfrac{-x}{-1} \geq \dfrac{-3}{-1}$

$\implies x \leq 3$

Answer 2

Step 1: Simplify both sides of the inequality.
-1/4 x+1/2 ≥ -1/4
Step 2: Subtract 1/2 from both sides.
-1/4 x+1/2 -1/2 ≥ -1/4 - 1/2
-1/4 x ≥ -3/4
Step 3: Multiply both sides by 4/(-1).
(4/-1)*(-1/4 x) ≥ ( 4/-1)*(-3/4)

The final answer is: x ≤ 3


Hope that helps you<3