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If 5x - 7 < 3x + 1, what is the range of x?

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Question: If 5x - 7 < 3x + 1, what is the range of x?

Options:

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

Correct Answer: x < 4

Solution: 

5x - 7 < 3x + 1 => 2x < 8 => x < 4.

If 5x - 7 < 3x + 1, what is the range of x?

Practice Questions

Q1
If 5x - 7 < 3x + 1, what is the range of x?
  1. x < 4
  2. x > 4
  3. x < 2
  4. x > 2

Questions & Step-by-Step Solutions

If 5x - 7 < 3x + 1, what is the range of x?
Correct Answer: x < 4
  • Step 1: Start with the inequality: 5x - 7 < 3x + 1.
  • Step 2: To isolate x, first subtract 3x from both sides: 5x - 3x - 7 < 1.
  • Step 3: This simplifies to: 2x - 7 < 1.
  • Step 4: Next, add 7 to both sides to get rid of -7: 2x < 1 + 7.
  • Step 5: This simplifies to: 2x < 8.
  • Step 6: Finally, divide both sides by 2 to solve for x: x < 4.
  • Inequalities – Understanding how to manipulate and solve inequalities involving variables.
  • Algebraic Manipulation – Skills in rearranging equations and isolating variables.
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