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Find the solution set for the inequality 6 - 2x ≤ 0.

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Question: Find the solution set for the inequality 6 - 2x ≤ 0.

Options:

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

Correct Answer: x > 3

Solution: 

6 - 2x ≤ 0 => -2x ≤ -6 => x ≥ 3.

Find the solution set for the inequality 6 - 2x ≤ 0.

Practice Questions

Q1
Find the solution set for the inequality 6 - 2x ≤ 0.
  1. x < 3
  2. x > 3
  3. x ≤ 3
  4. x ≥ 3

Questions & Step-by-Step Solutions

Find the solution set for the inequality 6 - 2x ≤ 0.
Correct Answer: x ≥ 3
  • Step 1: Start with the inequality: 6 - 2x ≤ 0.
  • Step 2: To isolate the term with x, subtract 6 from both sides: 6 - 2x - 6 ≤ 0 - 6.
  • Step 3: This simplifies to: -2x ≤ -6.
  • Step 4: Now, divide both sides by -2. Remember, when you divide by a negative number, you must flip the inequality sign: -2x / -2 ≥ -6 / -2.
  • Step 5: This simplifies to: x ≥ 3.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Applying operations to isolate the variable correctly, including handling negative signs.
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