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Difficulty: EasySolving Linear Inequalities

Which of the following inequalities represents the complete set of real values of xx that satisfy the inequality 15≤3−4x15 \leq 3 - 4x?

  1. A
    x≥−3x \geq -3
  2. B
    x≤−15x \leq -15
  3. C
    x≥−15x \geq -15
  4. x≤−3x \leq -3Answer
  5. E
    x≥3x \geq 3

Answer

The inequality x≤−3x \leq -3
Subtracting 3 from both sides of the inequality 15≤3−4x15 \leq 3 - 4x yields 12≤−4x12 \leq -4x. Dividing both sides by −4-4 and reversing the inequality sign results in −3≥x-3 \geq x, which is equivalent to x≤−3x \leq -3.

Step-by-Step Solution

1
Subtract 3 from both sides of the inequality.
12≤−4x12 \leq -4x
This isolates the variable term on the right side of the inequality.
2
Divide both sides of the inequality by −4-4 and reverse the inequality sign.
−3≥x-3 \geq x
Reversing the inequality sign is required whenever both sides of an inequality are multiplied or divided by a negative number.
3
Rewrite the inequality to place the variable on the left side.
x≤−3x \leq -3
Reorganizing the inequality with xx on the left side is the standard format for representing the solution set.

Key Concept

Solving linear inequalities by isolating the variable and reversing the inequality sign when dividing by a negative number.
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Topics

Solving Linear Inequalities

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