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Solve the inequality 4 - 2x ≤ 10. What is the solution?

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Question: Solve the inequality 4 - 2x ≤ 10. What is the solution?

Options:

  1. x ≥ -3
  2. x ≤ -3
  3. x > -3
  4. x < -3

Correct Answer: x ≥ -3

Solution: 

4 - 2x ≤ 10 => -2x ≤ 6 => x ≥ -3.

Solve the inequality 4 - 2x ≤ 10. What is the solution?

Practice Questions

Q1
Solve the inequality 4 - 2x ≤ 10. What is the solution?
  1. x ≥ -3
  2. x ≤ -3
  3. x > -3
  4. x < -3

Questions & Step-by-Step Solutions

Solve the inequality 4 - 2x ≤ 10. What is the solution?
Correct Answer: x ≥ -3
  • Step 1: Start with the inequality: 4 - 2x ≤ 10.
  • Step 2: Subtract 4 from both sides to isolate the term with x: -2x ≤ 10 - 4.
  • Step 3: Simplify the right side: -2x ≤ 6.
  • Step 4: Divide both sides by -2. Remember, when you divide by a negative number, you flip the inequality sign: x ≥ -3.
  • Inequalities – Understanding how to manipulate and solve inequalities involving linear expressions.
  • Algebraic Manipulation – Applying algebraic operations correctly to isolate the variable.
  • Reversing Inequalities – Recognizing when to reverse the inequality sign, particularly when multiplying or dividing by a negative number.
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