AlgebraMediumTwo descriptions of the same result
Algebra practice question
A number is doubled and then 7 is subtracted. The result is the same as when the number is halved and 8 is added. What is the number?
Answer: 10
Let the number be x: 2x − 7 = x/2 + 8. Subtract x/2: (3/2)x − 7 = 8, so (3/2)x = 15 and x = 10. Check: 20 − 7 = 13 and 5 + 8 = 13.
Common wrong answers
- If you answered 2
- 2 comes from 2x − 7 = x/2 + 8 solved as (3/2)x = 3 — the constants add to 15, not 3.
- If you answered 6
- 6 comes from 2x − 7 = x + 8 (halving the number was dropped); 2x − 7 = x/2 + 8.
- If you answered 15
- 15 is (3/2)x, one step short; multiply by 2/3.
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?
Not affiliated with the College Board. SAT is a trademark of the College Board.