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If 3(x - 1) < 2x + 4, what is the solution for x?

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Question: If 3(x - 1) < 2x + 4, what is the solution for x?

Options:

  1. x < 7
  2. x > 7
  3. x < 5
  4. x > 5

Correct Answer: x < 5

Solution: 

Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

If 3(x - 1) < 2x + 4, what is the solution for x?

Practice Questions

Q1
If 3(x - 1) < 2x + 4, what is the solution for x?
  1. x < 7
  2. x > 7
  3. x < 5
  4. x > 5

Questions & Step-by-Step Solutions

If 3(x - 1) < 2x + 4, what is the solution for x?
  • Step 1: Distribute the 3 into the parentheses: 3(x - 1) becomes 3x - 3. So the inequality is now 3x - 3 < 2x + 4.
  • Step 2: To get x by itself, subtract 2x from both sides of the inequality: 3x - 2x - 3 < 4. This simplifies to x - 3 < 4.
  • Step 3: Now, add 3 to both sides to isolate x: x - 3 + 3 < 4 + 3. This simplifies to x < 7.
  • Inequalities – Understanding how to manipulate and solve inequalities involving variables.
  • Distributive Property – Applying the distributive property to simplify expressions.
  • Algebraic Manipulation – Performing operations such as addition and subtraction to isolate the variable.
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