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Solve the inequality 4 - x ≤ 2x + 1. What is the solution?

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Question: Solve the inequality 4 - x ≤ 2x + 1. What is the solution?

Options:

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

Correct Answer: x ≤ 1

Solution: 

4 - x ≤ 2x + 1 => 3 ≤ 3x => x ≥ 1.

Solve the inequality 4 - x ≤ 2x + 1. What is the solution?

Practice Questions

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

Questions & Step-by-Step Solutions

Solve the inequality 4 - x ≤ 2x + 1. What is the solution?
Correct Answer: x ≥ 1
  • Step 1: Start with the inequality: 4 - x ≤ 2x + 1.
  • Step 2: To isolate x, first add x to both sides of the inequality. This gives you: 4 ≤ 2x + x + 1.
  • Step 3: Combine like terms on the right side: 4 ≤ 3x + 1.
  • Step 4: Next, subtract 1 from both sides to get: 4 - 1 ≤ 3x.
  • Step 5: Simplify the left side: 3 ≤ 3x.
  • Step 6: Finally, divide both sides by 3 to solve for x: 1 ≤ x.
  • Step 7: This can be rewritten as x ≥ 1.
  • Inequalities – Understanding how to manipulate and solve inequalities involving variables.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables.
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