Examkin

Question

Difficulty: EasySolving One-Variable Inequalities

Evaluate the following mathematical statement:

−4x+10≥−14-4x + 10 \geq -14

Which of the following represents the correct solution for xx?

  1. x≤6x \leq 6Answer
  2. B
    x≥6x \geq 6
  3. C
    x≤−6x \leq -6
  4. D
    x≤1x \leq 1

Answer

The correct answer is x≤6x \leq 6.
To solve the inequality, first subtract 1010 from both sides to get −4x≥−24-4x \geq -24. Next, isolate xx by dividing both sides by −4-4. Because you are dividing by a negative number, you must flip the inequality sign from ≥\geq to ≤\leq, resulting in x≤6x \leq 6.

Step-by-Step Solution

1
Subtract 1010 from both sides of the inequality.
−4x≥−24-4x \geq -24
This isolates the term containing the variable xx on one side of the inequality.
2
Divide both sides by −4-4 and reverse the inequality sign.
x≤6x \leq 6
When multiplying or dividing an inequality by a negative number, the direction of the inequality symbol must be flipped to maintain a true statement.

Key Concept

Solving one-variable inequalities requires the same algebraic steps as solving linear equations, with the critical exception that the inequality sign must be reversed when multiplying or dividing by a negative number.
Rate this question

Topics

Solving One-Variable Inequalities

More questions from this topic