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Find the solution set for the inequality 2(x - 1) ≥ 4.

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Question: Find the solution set for the inequality 2(x - 1) ≥ 4.

Options:

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

Correct Answer: x ≥ 3

Solution: 

2(x - 1) ≥ 4 => x - 1 ≥ 2 => x ≥ 3.

Find the solution set for the inequality 2(x - 1) ≥ 4.

Practice Questions

Q1
Find the solution set for the inequality 2(x - 1) ≥ 4.
  1. x < 3
  2. x > 3
  3. x ≤ 3
  4. x ≥ 3

Questions & Step-by-Step Solutions

Find the solution set for the inequality 2(x - 1) ≥ 4.
Correct Answer: x ≥ 3
  • Step 1: Start with the inequality: 2(x - 1) ≥ 4.
  • Step 2: Distribute the 2 on the left side: 2 * x - 2 * 1 ≥ 4, which simplifies to 2x - 2 ≥ 4.
  • Step 3: Add 2 to both sides of the inequality to isolate the term with x: 2x - 2 + 2 ≥ 4 + 2, which simplifies to 2x ≥ 6.
  • Step 4: Divide both sides by 2 to solve for x: 2x / 2 ≥ 6 / 2, which simplifies to x ≥ 3.
  • Inequalities – Understanding how to manipulate and solve inequalities, including isolating the variable.
  • Algebraic Manipulation – Applying distributive property and inverse operations to simplify and solve equations.
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