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Difficulty: EasyLinear Inequalities in One Variable

Which of the following represents all possible values of xx that satisfy the inequality −4(x+3)≤8-4(x + 3) \leq 8?

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

Answer

x≥−5x \geq -5
To solve −4(x+3)≤8-4(x + 3) \leq 8, first distribute the −4-4 to obtain −4x−12≤8-4x - 12 \leq 8. Next, add 1212 to both sides to isolate the variable term, resulting in −4x≤20-4x \leq 20. Finally, divide both sides by −4-4 and reverse the inequality sign because of division by a negative number, which yields x≥−5x \geq -5.

Step-by-Step Solution

1
Distribute the coefficient outside the parentheses to the terms inside.
−4x−12≤8-4x - 12 \leq 8
Multiplying −4-4 by xx and −4-4 by 33 simplifies the left side of the inequality.
2
Isolate the variable term by adding 1212 to both sides of the inequality.
−4x≤20-4x \leq 20
Adding 1212 eliminates the constant term on the left side: 8+12=208 + 12 = 20.
3
Divide both sides of the inequality by −4-4 and reverse the inequality sign.
x≥−5x \geq -5
Dividing by a negative number reverses the direction of the inequality symbol: 20/−4=−520 / -4 = -5.

Key Concept

Solving linear inequalities in one variable using the distributive property and division by a negative number.
Estimated Time:45s
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Topics

Linear Inequalities in One Variable

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