Question

What is the solution to the given inequality?½-½ x ²-1/O x₂ -1O xs-1O x ≥ 3O x≤ 3IntroSolve the inequality.1---X24Apply properties:AddMultiplySubtractDivideTo start over:ResetDone

Answer 1

Answer:

x ≤ 3

Explanation:

The given inequality is

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

To solve the inequality, we first need to subtract 1/2 from both sides

$\begin{gathered} \frac{1}{2}-\frac{1}{4}x-\frac{1}{2}\ge-\frac{1}{4}-\frac{1}{2} \\ \\ -\frac{1}{4}x\ge-\frac{3}{4} \end{gathered}$

Then, multiply both sides by -4. Since -4 is a negative number, the symbol of the inequality changes, so

$\begin{gathered} (-4)(-\frac{1}{4}x)\leq(-4)(-\frac{3}{4}) \\ \\ x\leq3 \end{gathered}$

Therefore, the answer is

x ≤ 3