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Question

Difficulty: EasyLinear Inequalities in One Variable

Which of the following inequalities is equivalent to −3(x−4)<15-3(x - 4) < 15?

  1. x>−1x > -1Answer
  2. B
    x<−1x < -1
  3. C
    x>−9x > -9
  4. D
    x<−9x < -9

Answer

The inequality x>−1x > -1
The correct answer is obtained by dividing both sides of the inequality −3(x−4)<15-3(x - 4) < 15 by −3-3, which reverses the inequality symbol to yield x−4>−5x - 4 > -5. Adding 44 to both sides isolates the variable, resulting in x>−1x > -1. Alternatively, distributing the −3-3 first yields −3x+12<15-3x + 12 < 15, which simplifies to −3x<3-3x < 3, and dividing by −3-3 with a sign flip yields x>−1x > -1.

Step-by-Step Solution

1
Divide both sides of the inequality −3(x−4)<15-3(x - 4) < 15 by −3-3.
x−4>−5x - 4 > -5
Dividing an inequality by a negative number reverses the direction of the inequality symbol.
2
Add 44 to both sides of the inequality to isolate xx.
x>−1x > -1
Adding a constant to both sides preserves the inequality and isolates the variable xx.

Key Concept

Solving linear inequalities in one variable involving distribution and negative coefficients.
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Topics

Linear Inequalities in One Variable

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