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Solve the inequality 3(x - 1) < 2(x + 2). What is the solution?

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Question: Solve the inequality 3(x - 1) < 2(x + 2). What is the solution?

Options:

  1. x < 5
  2. x > 5
  3. x < 4
  4. x > 4

Correct Answer: x < 4

Solution: 

3(x - 1) < 2(x + 2) => 3x - 3 < 2x + 4 => x < 7

Solve the inequality 3(x - 1) < 2(x + 2). What is the solution?

Practice Questions

Q1
Solve the inequality 3(x - 1) < 2(x + 2). What is the solution?
  1. x < 5
  2. x > 5
  3. x < 4
  4. x > 4

Questions & Step-by-Step Solutions

Solve the inequality 3(x - 1) < 2(x + 2). What is the solution?
  • Step 1: Start with the inequality: 3(x - 1) < 2(x + 2).
  • Step 2: Distribute the 3 on the left side: 3 * x - 3 * 1 = 3x - 3.
  • Step 3: Distribute the 2 on the right side: 2 * x + 2 * 2 = 2x + 4.
  • Step 4: Now the inequality looks like this: 3x - 3 < 2x + 4.
  • Step 5: To isolate x, subtract 2x from both sides: 3x - 2x - 3 < 4.
  • Step 6: This simplifies to: x - 3 < 4.
  • Step 7: Now, add 3 to both sides to solve for x: x < 4 + 3.
  • Step 8: This gives us the final solution: x < 7.
  • Inequalities – Understanding how to manipulate and solve inequalities involving variables.
  • Algebraic Manipulation – Skills in distributing, combining like terms, and isolating the variable.
  • Solution Interpretation – Interpreting the solution of an inequality in terms of the variable.
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