Question

solve the inequality for x.
5 - 4x ≥ 13 - 2x
simplify your answer as much as possible.

Explanation:

Step1: Add \(2x\) to both sides

To eliminate the \(x\) term on the right, we add \(2x\) to both sides of the inequality \(5 - 4x \geq 13 - 2x\). This gives \(5 - 4x + 2x \geq 13 - 2x + 2x\), which simplifies to \(5 - 2x \geq 13\).

Step2: Subtract 5 from both sides

Next, we subtract 5 from both sides to isolate the term with \(x\). So, \(5 - 2x - 5 \geq 13 - 5\), which simplifies to \(-2x \geq 8\).

Step3: Divide by -2 (and reverse inequality)

When we divide both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing \(-2x \geq 8\) by \(-2\) gives \(x \leq -4\) (since dividing by a negative number flips the inequality from \(\geq\) to \(\leq\)).

Answer:

\(x \leq -4\)