Question

challenge #3
solve this inequality to help shira eat all the grass.
$-\frac{1}{2}x + 2 \leq 3$

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( x \), we subtract 2 from both sides of the inequality \( -\frac{1}{2}x + 2 \leq 3 \). This gives us \( -\frac{1}{2}x + 2 - 2 \leq 3 - 2 \), which simplifies to \( -\frac{1}{2}x \leq 1 \).

Step2: Multiply both sides by -2 (and reverse inequality)

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So we multiply both sides of \( -\frac{1}{2}x \leq 1 \) by -2. This gives \( (-2)\times(-\frac{1}{2}x) \geq 1\times(-2) \) (note the reversed inequality sign). Simplifying the left side, \( (-2)\times(-\frac{1}{2}x)=x \), and the right side is -2. So we get \( x \geq -2 \).

Answer:

\( x \geq -2 \)