Question

solve for $x$ and graph the solution on the number line below.

$-2x - 5 geq 3$ or $-7 > -2x - 5$

answer attempt 1 out of 3

$<>leqgeq$ or

inequality notation:

number line:

Explanation:

Step1: Solve the first inequality

Solve $-2x - 5\geq3$.
Add 5 to both sides: $-2x\geq3 + 5$, so $-2x\geq8$.
Divide both sides by -2 (and reverse the inequality sign): $x\leq - 4$.

Step2: Solve the second inequality

Solve $-7>-2x - 5$.
Add 5 to both sides: $-7 + 5>-2x$, so $-2>-2x$.
Divide both sides by -2 (and reverse the inequality sign): $1 1$.

Answer:

Inequality Notation: $x\leq - 4$ or $x>1$

For the number line:

• For $x\leq - 4$: Draw a closed circle at -4 and shade to the left.
• For $x>1$: Draw an open circle at 1 and shade to the right.