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If 3x + 2 < 5x - 6, what is the range of x?

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Question: If 3x + 2 < 5x - 6, what is the range of x?

Options:

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

Correct Answer: x > 4

Solution: 

Rearranging gives 8 < 2x, thus x > 4.

If 3x + 2 < 5x - 6, what is the range of x?

Practice Questions

Q1
If 3x + 2 < 5x - 6, what is the range of x?
  1. x < 4
  2. x > 4
  3. x = 4
  4. x < 3

Questions & Step-by-Step Solutions

If 3x + 2 < 5x - 6, what is the range of x?
  • Step 1: Start with the inequality 3x + 2 < 5x - 6.
  • Step 2: To isolate x, first subtract 3x from both sides. This gives you 2 < 5x - 3x - 6.
  • Step 3: Simplify the right side. You get 2 < 2x - 6.
  • Step 4: Next, add 6 to both sides to move the -6. This results in 2 + 6 < 2x.
  • Step 5: Simplify the left side. You now have 8 < 2x.
  • Step 6: Finally, divide both sides by 2 to solve for x. This gives you 4 < x.
  • Step 7: Rewrite the inequality as x > 4.
  • Inequalities – Understanding how to manipulate and solve inequalities.
  • Algebraic Rearrangement – Rearranging equations to isolate the variable.
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