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Determine the solution set for the inequality 7x + 3 < 4x + 12.

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Question: Determine the solution set for the inequality 7x + 3 < 4x + 12.

Options:

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

Correct Answer: x > 3

Solution: 

7x + 3 < 4x + 12 => 3x < 9 => x < 3.

Determine the solution set for the inequality 7x + 3 < 4x + 12.

Practice Questions

Q1
Determine the solution set for the inequality 7x + 3 < 4x + 12.
  1. x < 3
  2. x > 3
  3. x ≤ 3
  4. x ≥ 3

Questions & Step-by-Step Solutions

Determine the solution set for the inequality 7x + 3 < 4x + 12.
Correct Answer: x < 3
  • Step 1: Start with the inequality: 7x + 3 < 4x + 12.
  • Step 2: To isolate the variable x, subtract 4x from both sides: 7x - 4x + 3 < 12.
  • Step 3: This simplifies to: 3x + 3 < 12.
  • Step 4: Next, subtract 3 from both sides: 3x < 12 - 3.
  • Step 5: This simplifies to: 3x < 9.
  • Step 6: Finally, divide both sides by 3 to solve for x: x < 9 / 3.
  • Step 7: This gives us the final solution: x < 3.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Skills in isolating the variable and simplifying expressions.
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