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Solve the inequality: -2(x + 3) > 4.

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Question: Solve the inequality: -2(x + 3) > 4.

Options:

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

Correct Answer: x < -7

Solution: 

Step 1: Distribute -2: -2x - 6 > 4. Step 2: Add 6: -2x > 10. Step 3: Divide by -2 (reverse inequality): x < -5.

Solve the inequality: -2(x + 3) > 4.

Practice Questions

Q1
Solve the inequality: -2(x + 3) > 4.
  1. x < -1
  2. x > -1
  3. x < -7
  4. x > -7

Questions & Step-by-Step Solutions

Solve the inequality: -2(x + 3) > 4.
  • Step 1: Distribute -2 to both terms inside the parentheses: -2(x + 3) becomes -2x - 6. So, the inequality is now -2x - 6 > 4.
  • Step 2: Add 6 to both sides of the inequality to isolate the term with x. This gives us -2x > 10.
  • Step 3: Divide both sides by -2. Remember, when you divide by a negative number, you must reverse the inequality sign. So, x < -5.
  • Inequalities – Understanding how to manipulate and solve inequalities, including the effect of multiplying or dividing by negative numbers.
  • Distributive Property – Applying the distributive property to simplify expressions before solving.
  • Reversing Inequality – Recognizing that the direction of the inequality changes when dividing or multiplying by a negative number.
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