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Question

Difficulty: EasySolving One-Variable Inequalities

Consider the following one-variable inequality:

12−3x≤2712 - 3x \leq 27

Which of the following represents the correct solution set for xx?

  1. x≥−5x \geq -5Answer
  2. B
    x≤−5x \leq -5
  3. C
    x≥5x \geq 5
  4. D
    x≥−13x \geq -13

Answer

x≥−5x \geq -5
To solve the inequality, first subtract 12 from both sides to get −3x≤15-3x \leq 15. Next, divide both sides by -3. Because the division involves a negative number, the direction of the inequality symbol must be reversed, resulting in the correct solution of x≥−5x \geq -5.

Step-by-Step Solution

1
Subtract 1212 from both sides of the inequality.
−3x≤15-3x \leq 15
This step isolates the term containing the variable on one side of the inequality.
2
Divide both sides by −3-3 and reverse the inequality symbol.
x≥−5x \geq -5
According to the rules of algebra, whenever you multiply or divide an inequality by a negative number, the direction of the inequality sign must be flipped.

Key Concept

Solving One-Variable Inequalities
Estimated Time:45s
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Topics

Solving One-Variable Inequalities

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