AlgebraMediumCounting integers in a compound inequality
Algebra practice question
How many integer values of x satisfy 5 < 3x − 4 < 17?
Answer: 3
Add 4: 9 < 3x < 21. Divide by 3: 3 < x < 7. The integers are 4, 5, and 6: three values.
Common wrong answers
- If you answered 4
- 4 includes one endpoint.
- If you answered 5
- 5 counts 3 and 7, but both endpoints are excluded.
- If you answered 12
- 12 is 21 − 9, the width before dividing by 3.
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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