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Determine the solution set for the inequality 2(x - 1) ≥ 3.

Practice Questions

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

Questions & Step-by-Step Solutions

Determine the solution set for the inequality 2(x - 1) ≥ 3.
Correct Answer: x ≥ 2
  • Step 1: Start with the inequality: 2(x - 1) ≥ 3.
  • Step 2: Distribute the 2 on the left side: 2 * x - 2 * 1 ≥ 3, which simplifies to 2x - 2 ≥ 3.
  • Step 3: Add 2 to both sides of the inequality to isolate the term with x: 2x - 2 + 2 ≥ 3 + 2, which simplifies to 2x ≥ 5.
  • Step 4: Divide both sides by 2 to solve for x: 2x / 2 ≥ 5 / 2, which simplifies to x ≥ 2.5.
  • Inequalities – Understanding how to manipulate and solve inequalities, including isolating the variable.
  • Distributive Property – Applying the distributive property correctly when expanding expressions.
  • Solution Sets – Identifying the correct solution set for the inequality after solving.
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