Question

solve the inequality and graph the solution on the line provided.
-2x - 5 ≥ -21
answer
inequality notation:
number line:

Explanation:

Step1: Add 5 to both sides

To isolate the term with \( x \), we add 5 to both sides of the inequality \(-2x - 5 \geq -21\). This gives us \(-2x - 5 + 5 \geq -21 + 5\), which simplifies to \(-2x \geq -16\).

Step2: Divide by -2 (reverse inequality)

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \(-2x \geq -16\) by \(-2\) gives \(x \leq \frac{-16}{-2}\), which simplifies to \(x \leq 8\).

Answer:

Inequality Notation: \( x \leq 8 \)

For the number line: Place a closed circle at 8 (since the inequality is "less than or equal to") and draw a line to the left of 8 to represent all values of \( x \) that satisfy the inequality.