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Difficulty: EasyLinear Inequalities in One Variable

Which of the following represents all possible values of xx that satisfy the inequality −2(x−5)>6-2(x - 5) > 6?

  1. A
    x<−8x < -8
  2. x<2x < 2Answer
  3. C
    x>2x > 2
  4. D
    x<8x < 8

Answer

The inequality is satisfied when x<2x < 2.
Dividing both sides of the inequality −2(x−5)>6-2(x - 5) > 6 by −2-2 yields x−5<−3x - 5 < -3, where the inequality sign is reversed because of division by a negative number. Adding 55 to both sides of x−5<−3x - 5 < -3 results in x<2x < 2.

Step-by-Step Solution

1
Divide both sides of the inequality −2(x−5)>6-2(x - 5) > 6 by −2-2.
x−5<−3x - 5 < -3
Dividing both sides of an inequality by a negative number requires reversing the direction of the inequality sign.
2
Add 55 to both sides of the inequality to isolate xx.
x<2x < 2
To solve for xx, eliminate the constant term −5-5 on the left side of the inequality.

Key Concept

Solving linear inequalities in one variable, including reversing the inequality sign when multiplying or dividing by a negative number.
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Topics

Linear Inequalities in One Variable

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