Questions: Graph the inequality and give interval notation for the solution. Use two o's (as in octop) and a U for union as needed. -4x + 6 > 18 OR -9x + 3 ≤ 21

Transcript text: Graph the inequality and give interval notation for the solution. Use two o's (as in octop a $U$ for union as needed. \[ -4 x+6>18 \text { OR }-9 x+3 \leq 21 \]

Solution

Solution Steps

Step 1: Solve the first inequality $-4x + 6 > 18$

Subtract 6 from both sides: \[ -4x > 12 \] Divide both sides by -4 (and reverse the inequality sign): \[ x < -3 \]

Step 2: Solve the second inequality $-9x + 3 \leq 21$

Subtract 3 from both sides: \[ -9x \leq 18 \] Divide both sides by -9 (and reverse the inequality sign): \[ x \geq -2 \]

Step 3: Combine the solutions using union

The solution to the compound inequality is: \[ x < -3 \quad \text{OR} \quad x \geq -2 \]

Final Answer

The interval notation for the solution is: \[ (-\infty, -3) \cup [-2, \infty) \]

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