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Difficulty: EasyLinear Inequalities and Absolute Value

If −5x+3≤18-5x + 3 \le 18, which of the following inequalities represents all possible real values of xx?

  1. x≥−3x \ge -3Answer
  2. B
    x≤−3x \le -3
  3. C
    x≥3x \ge 3
  4. D
    x≤3x \le 3
  5. E
    x≥−215x \ge -\frac{21}{5}

Answer

x≥−3x \ge -3
Subtracting 3 from both sides gives −5x≤15-5x \le 15. Dividing both sides by −5-5 requires flipping the inequality sign from ≤\le to ≥\ge, resulting in x≥−3x \ge -3.

Step-by-Step Solution

1
Subtract 3 from both sides of the inequality −5x+3≤18-5x + 3 \le 18.
−5x≤15-5x \le 15
Isolate the variable term on the left side.
2
Divide both sides by −5-5 and reverse the inequality sign from ≤\le to ≥\ge.
x≥−3x \ge -3
Dividing an inequality by a negative number reverses the direction of the inequality sign.

Key Concept

Linear Inequalities and Sign Reversal
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Topics

Linear Inequalities and Absolute Value

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