AlgebraMediumCounting integers in a compound inequality
Algebra practice question
How many integers x satisfy −2 < x + 3 ≤ 5?
Answer: 7
Subtracting 3 gives −5 < x ≤ 2, so x can be −4, −3, −2, −1, 0, 1, or 2.
Common wrong answers
- If you answered 5
- 5 counts only −2 through 2, forgetting to subtract 3.
- If you answered 6
- 6 leaves out 2, which the ≤ allows.
- If you answered 8
- 8 includes −5, but the left inequality is strict.
More Algebra questions
- Medium
A system: 2x + y = 11 and x − y = 1. What is the value of x + y? - Medium
Which of the following describes all solutions to 4x − 9 ≤ 2x + 5? - Medium
A phone's battery percentage is modeled by P = 100 − 8t, where t is the number of hours since it was unplugged… - Medium
If y = 2x − 1 and 3x + y = 14, what is the value of x? - Medium
If |2x − 3| = 7, what is the sum of all possible values of x? - Medium
Line k has equation y = (2/3)x + 1. Which equation represents a line perpendicular to line k?
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