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

x ≤ 3

Step-by-step explanation:

The given inequality is

`(1)/(2)-(1)/(4)x\ge-(1)/(4)`

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

`\begin{gathered} (1)/(2)-(1)/(4)x-(1)/(2)\ge-(1)/(4)-(1)/(2) \\ \\ -(1)/(4)x\ge-(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)(-(1)/(4)x)\leq(-4)(-(3)/(4)) \\ \\ x\leq3 \end{gathered}`

Therefore, the answer is

x ≤ 3