Questions: Solve the compound inequality. 3x - 2 ≤ 13 and 3x - 3 ≥ -12 Graph the solution on the number line.

Solve the compound inequality. 3x - 2 ≤ 13 and 3x - 3 ≥ -12 Graph the solution on the number line.
Transcript text: Solve the compound inequality. \[ 3 x-2 \leq 13 \text { and } 3 x-3 \geq-12 \] Graph the solution on the number line.
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Solution

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Solution Steps

Step 1: Solve the first inequality \(3x - 2 \leq 13\)

Add 2 to both sides: \[ 3x - 2 + 2 \leq 13 + 2 \] \[ 3x \leq 15 \]

Divide both sides by 3: \[ x \leq 5 \]

Step 2: Solve the second inequality \(3x - 3 \geq -12\)

Add 3 to both sides: \[ 3x - 3 + 3 \geq -12 + 3 \] \[ 3x \geq -9 \]

Divide both sides by 3: \[ x \geq -3 \]

Step 3: Combine the solutions

The solution to the compound inequality is: \[ -3 \leq x \leq 5 \]

Step 4: Graph the solution on the number line
  • Draw a number line.
  • Mark and shade the region between -3 and 5, including -3 and 5 (closed circles).

Final Answer

The solution to the compound inequality is \(-3 \leq x \leq 5\). The graph on the number line is a shaded region from -3 to 5, including the endpoints.

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