Question

u2:04: unit 2 test
which inequality describes the graph?
(the graph is a number line with a filled dot at 10 and an arrow pointing to the left, with marks at -20, -10, 0, 10, 20, 30)
options:
-3x ≥ -30
-3x ≤ 30
3x ≤ -30
-3x > -30

Explanation:

Step1: Analyze the graph

The graph has a closed dot at 10 and the line is shaded to the left, so the inequality is \( x \leq 10 \).

Step2: Solve each option

• Option 1: \( -3x \geq -30 \)

Divide both sides by -3 (reverse inequality): \( x \leq 10 \). Matches the graph.

• Option 2: \( -3x \leq 30 \)

Divide by -3 (reverse inequality): \( x \geq -10 \). Does not match.

• Option 3: \( 3x \leq -30 \)

Divide by 3: \( x \leq -10 \). Does not match.

• Option 4: \( -3x > -30 \)

Divide by -3 (reverse inequality): \( x < 10 \). Open dot, does not match.

Answer:

\( -3x \geq -30 \) (the first option)