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What is the solution to the compound inequality 1 < 2x + 3 < 7?

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Question: What is the solution to the compound inequality 1 < 2x + 3 < 7?

Options:

  1. -1 < x < 2
  2. 0 < x < 2
  3. 1 < x < 2
  4. 1 < x < 3

Correct Answer: -1 < x < 2

Solution: 

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

What is the solution to the compound inequality 1 < 2x + 3 < 7?

Practice Questions

Q1
What is the solution to the compound inequality 1 < 2x + 3 < 7?
  1. -1 < x < 2
  2. 0 < x < 2
  3. 1 < x < 2
  4. 1 < x < 3

Questions & Step-by-Step Solutions

What is the solution to the compound inequality 1 < 2x + 3 < 7?
Correct Answer: -1 < x < 2
  • Step 1: Start with the compound inequality: 1 < 2x + 3 < 7.
  • Step 2: To isolate 2x, subtract 3 from all parts of the inequality: 1 - 3 < 2x + 3 - 3 < 7 - 3.
  • Step 3: Simplify the inequality: -2 < 2x < 4.
  • Step 4: Now, divide all parts of the inequality by 2 to solve for x: -2 / 2 < 2x / 2 < 4 / 2.
  • Step 5: Simplify again: -1 < x < 2.
  • Step 6: The solution to the compound inequality is -1 < x < 2.
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