Question

u2:04: unit 2 test
which inequality describes the graph?
-20 -10 0 10 20 30
○ $3x \leq -30$
○ $-3x < 30$
○ $-3x > -30$
○ $-3x < -30$

Explanation:

Step1: Analyze the graph

The graph has an open circle at 10 and the arrow points to the left, so the inequality represents \(x < 10\) (open circle means not including 10, arrow left means less than).

Step2: Solve each option

• Option 1: \(3x \leq - 30\), divide both sides by 3: \(x \leq - 10\). Doesn't match.
• Option 2: \(-3x < 30\), divide both sides by - 3 (reverse inequality): \(x > - 10\). Doesn't match.
• Option 3: \(-3x > - 30\), divide both sides by - 3 (reverse inequality): \(x < 10\). Matches the graph.
• Option 4: \(-3x < - 30\), divide both sides by - 3 (reverse inequality): \(x > 10\). Doesn't match.

Answer:

\(-3x > - 30\) (the third option)