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Find the solution set for the inequality 2x + 1 ≤ 3x - 4.

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Question: Find the solution set for the inequality 2x + 1 ≤ 3x - 4.

Options:

  1. x < 5
  2. x > 5
  3. x ≤ 5
  4. x ≥ 5

Correct Answer: x ≤ 5

Solution: 

2x + 1 ≤ 3x - 4 => 1 + 4 ≤ x => x ≥ 5.

Find the solution set for the inequality 2x + 1 ≤ 3x - 4.

Practice Questions

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

Questions & Step-by-Step Solutions

Find the solution set for the inequality 2x + 1 ≤ 3x - 4.
Correct Answer: x ≥ 5
  • Step 1: Start with the inequality: 2x + 1 ≤ 3x - 4.
  • Step 2: To isolate x, first subtract 2x from both sides: 1 ≤ 3x - 2x - 4.
  • Step 3: This simplifies to: 1 ≤ x - 4.
  • Step 4: Next, add 4 to both sides to isolate x: 1 + 4 ≤ x.
  • Step 5: This simplifies to: 5 ≤ x.
  • Step 6: We can also write this as: x ≥ 5.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables.
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