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Solve the inequality 7x - 4 < 2x + 11. What is the solution?

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Question: Solve the inequality 7x - 4 < 2x + 11. What is the solution?

Options:

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

Correct Answer: x > 3

Solution: 

7x - 4 < 2x + 11 => 5x < 15 => x < 3.

Solve the inequality 7x - 4 < 2x + 11. What is the solution?

Practice Questions

Q1
Solve the inequality 7x - 4 < 2x + 11. What is the solution?
  1. x < 3
  2. x > 3
  3. x ≤ 3
  4. x ≥ 3

Questions & Step-by-Step Solutions

Solve the inequality 7x - 4 < 2x + 11. What is the solution?
Correct Answer: x < 3
  • Step 1: Start with the inequality: 7x - 4 < 2x + 11.
  • Step 2: To get all the x terms on one side, subtract 2x from both sides: 7x - 2x - 4 < 11.
  • Step 3: Simplify the left side: 5x - 4 < 11.
  • Step 4: Next, add 4 to both sides to isolate the term with x: 5x < 11 + 4.
  • Step 5: Simplify the right side: 5x < 15.
  • Step 6: Finally, divide both sides by 5 to solve for x: x < 15 / 5.
  • Step 7: Simplify the right side: x < 3.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Skills in isolating the variable and performing operations on both sides of the inequality.
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