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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