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Determine the solution set for the inequality 6x - 4 < 2x + 8.

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Question: Determine the solution set for the inequality 6x - 4 < 2x + 8.

Options:

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

Correct Answer: x > 3

Solution: 

6x - 4 < 2x + 8 => 4x < 12 => x < 3.

Determine the solution set for the inequality 6x - 4 < 2x + 8.

Practice Questions

Q1
Determine the solution set for the inequality 6x - 4 < 2x + 8.
  1. x < 3
  2. x > 3
  3. x < 2
  4. x > 2

Questions & Step-by-Step Solutions

Determine the solution set for the inequality 6x - 4 < 2x + 8.
Correct Answer: x < 3
  • Step 1: Start with the inequality: 6x - 4 < 2x + 8.
  • Step 2: To get all the x terms on one side, subtract 2x from both sides: 6x - 2x - 4 < 8.
  • Step 3: Simplify the left side: 4x - 4 < 8.
  • Step 4: Next, add 4 to both sides to isolate the term with x: 4x < 8 + 4.
  • Step 5: Simplify the right side: 4x < 12.
  • Step 6: Finally, divide both sides by 4 to solve for x: x < 12 / 4.
  • Step 7: Simplify the right side: x < 3.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables.
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