Question:
The set of all \( x \) satisfying the inequalities \( -4 \le 2 - 3x<7 \) is
The set of all \( x \) satisfying the inequalities \( -4 \le 2 - 3x<7 \) is
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Remember: inequality sign reverses when multiplying or dividing by a negative number.
Updated On: Apr 21, 2026
- \( (2, \frac{5}{3}) \)
- \( [2, \frac{5}{3}) \)
- \( [-\frac{11}{3}, 2] \)
- \( [-\frac{5}{3}, 2] \)
- \( (-\frac{7}{3}, 2) \)
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The Correct Option is D
Solution and Explanation
Concept:
Solve compound inequalities step-by-step.
Step 1: Split inequality.
\[ -4 \le 2 - 3x \quad \text{and} \quad 2 - 3x<7 \]
Step 2: Solve first inequality.
\[ -4 \le 2 - 3x \] \[ -6 \le -3x \Rightarrow 2 \ge x \]
Step 3: Solve second inequality.
\[ 2 - 3x<7 \] \[ -3x -\frac{5}{3} \]
Step 4: Combine results.
\[ -\frac{5}{3}<x \le 2 \] \[ \Rightarrow [-\frac{5}{3}, 2] \]
Step 1: Split inequality.
\[ -4 \le 2 - 3x \quad \text{and} \quad 2 - 3x<7 \]
Step 2: Solve first inequality.
\[ -4 \le 2 - 3x \] \[ -6 \le -3x \Rightarrow 2 \ge x \]
Step 3: Solve second inequality.
\[ 2 - 3x<7 \] \[ -3x -\frac{5}{3} \]
Step 4: Combine results.
\[ -\frac{5}{3}<x \le 2 \] \[ \Rightarrow [-\frac{5}{3}, 2] \]
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