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

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Question: Solve the inequality 2(x - 1) > 3x + 4. What is the solution?

Options:

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

Correct Answer: x < -1

Solution: 

2(x - 1) > 3x + 4 => 2x - 2 > 3x + 4 => -x > 6 => x < -6.

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

Practice Questions

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

Questions & Step-by-Step Solutions

Solve the inequality 2(x - 1) > 3x + 4. What is the solution?
Correct Answer: x < -6
  • Step 1: Start with the inequality: 2(x - 1) > 3x + 4.
  • Step 2: Distribute the 2 on the left side: 2 * x - 2 * 1 > 3x + 4, which simplifies to 2x - 2 > 3x + 4.
  • Step 3: Now, we want to get all the x terms on one side. Subtract 3x from both sides: 2x - 2 - 3x > 4.
  • Step 4: This simplifies to -x - 2 > 4.
  • Step 5: Next, add 2 to both sides to isolate the x term: -x > 4 + 2.
  • Step 6: This simplifies to -x > 6.
  • Step 7: To solve for x, multiply both sides by -1. Remember, when you multiply or divide by a negative number, you flip the inequality sign: x < -6.
  • Inequalities – Understanding how to manipulate and solve inequalities involving variables.
  • Algebraic Manipulation – Skills in distributing, combining like terms, and isolating variables.
  • Direction of Inequality – Recognizing how the direction of the inequality changes when multiplying or dividing by negative numbers.
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