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Solve the inequality 7x + 2 < 3x + 10.

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Question: Solve the inequality 7x + 2 < 3x + 10.

Options:

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

Correct Answer: x > 2

Solution: 

7x + 2 < 3x + 10 => 4x < 8 => x < 2.

Solve the inequality 7x + 2 < 3x + 10.

Practice Questions

Q1
Solve the inequality 7x + 2 < 3x + 10.
  1. x < 2
  2. x > 2
  3. x ≤ 2
  4. x ≥ 2

Questions & Step-by-Step Solutions

Solve the inequality 7x + 2 < 3x + 10.
Correct Answer: x < 2
  • Step 1: Start with the inequality: 7x + 2 < 3x + 10.
  • Step 2: To get all the x terms on one side, subtract 3x from both sides: 7x - 3x + 2 < 10.
  • Step 3: This simplifies to: 4x + 2 < 10.
  • Step 4: Now, subtract 2 from both sides to isolate the term with x: 4x < 10 - 2.
  • Step 5: This simplifies to: 4x < 8.
  • Step 6: Finally, divide both sides by 4 to solve for x: x < 8 / 4.
  • Step 7: This gives us the final answer: x < 2.
  • Linear Inequalities – The question tests the ability to solve linear inequalities by isolating the variable.
  • Algebraic Manipulation – It assesses skills in rearranging and simplifying expressions correctly.
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