Question

question
solve for x and graph the solution on the number line below.
-2x - 5 ≥ 3 or -7 > -2x - 5
answer
inequality notation:
number line:

Explanation:

Step1: Solve \(-2x - 5 \geq 3\)

Add 5 to both sides: \(-2x - 5 + 5 \geq 3 + 5\) → \(-2x \geq 8\)
Divide by -2 (reverse inequality): \(x \leq -4\)

Step2: Solve \(-7 > -2x - 5\)

Add 5 to both sides: \(-7 + 5 > -2x - 5 + 5\) → \(-2 > -2x\)
Divide by -2 (reverse inequality): \(1 < x\) (or \(x > 1\))

Step3: Combine solutions (OR)

The solution is \(x \leq -4\) or \(x > 1\).

Answer:

Inequality Notation: \(x \leq -4\) or \(x > 1\)
(For the number line: Plot a closed circle at \(-4\) and shade left, open circle at \(1\) and shade right.)