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Find the solution set for the inequality 2x + 5 ≤ 3x - 1.

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Question: Find the solution set for the inequality 2x + 5 ≤ 3x - 1.

Options:

  1. x ≤ 6
  2. x ≥ 6
  3. x < 6
  4. x > 6

Correct Answer: x < 6

Solution: 

2x + 5 ≤ 3x - 1 => 5 + 1 ≤ 3x - 2x => 6 ≤ x => x ≥ 6.

Find the solution set for the inequality 2x + 5 ≤ 3x - 1.

Practice Questions

Q1
Find the solution set for the inequality 2x + 5 ≤ 3x - 1.
  1. x ≤ 6
  2. x ≥ 6
  3. x < 6
  4. x > 6

Questions & Step-by-Step Solutions

Find the solution set for the inequality 2x + 5 ≤ 3x - 1.
  • Step 1: Start with the inequality: 2x + 5 ≤ 3x - 1.
  • Step 2: To isolate x, first move all terms involving x to one side. Subtract 2x from both sides: 5 ≤ 3x - 2x - 1.
  • Step 3: Simplify the right side: 5 ≤ x - 1.
  • Step 4: Now, add 1 to both sides to isolate x: 5 + 1 ≤ x.
  • Step 5: Simplify the left side: 6 ≤ x.
  • Step 6: This can be rewritten as x ≥ 6, which is the solution set.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables.
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