Questions: Which graph represents the solution set for the compound inequality below? -1/3 x+10 >= 7 x-10 >= 7

Transcript text: Which graph represents the solution set for the compound inequality below? \[ \begin{array}{l} -\frac{1}{3} x+10 \geq 7 \\ x-10 \geq 7 \end{array} \]

Solution

Solution Steps

Step 1: Solve the first inequality

The first inequality is: \[ -\frac{1}{3}x + 10 \geq 7 \]

Subtract 10 from both sides: \[ -\frac{1}{3}x \geq -3 \]

Multiply both sides by -3 (and reverse the inequality sign because we are multiplying by a negative number): \[ x \leq 9 \]

Step 2: Solve the second inequality

The second inequality is: \[ x - 10 \geq 7 \]

Add 10 to both sides: \[ x \geq 17 \]

Step 3: Combine the inequalities

The solution set for the compound inequality is: \[ x \leq 9 \quad \text{or} \quad x \geq 17 \]

Final Answer

The graph that represents the solution set for the compound inequality is the third one, which shows \( x \leq 9 \) or \( x \geq 17 \).

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