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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 move all x terms to one side. Add x to both sides: 4 > 2x + 1 + x.
  • Step 3: Simplify the right side: 4 > 3x + 1.
  • Step 4: Now, subtract 1 from both sides to isolate the term with x: 4 - 1 > 3x.
  • Step 5: This simplifies to: 3 > 3x.
  • Step 6: Next, divide both sides by 3 to solve for x: 3/3 > x.
  • Step 7: This simplifies to: 1 > x, or 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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