Max@Math Revolution wrote:Which of the following is satisfied with |x-4|+|x-3|<2?
A. 1<x<5
B. 2<x<5
C. 2.5<x<4.5
D. 2.5<x<4
E. 3<x<4
D and E imply that x must be LESS than 4, while A, B and C imply that x can be GREATER than 4.
Test x=4.1.
If we plug x=4.1 into |x-4|+|x-3|<2, we get:
|4.1 - 4| + |4.1 - 3| < 2
0.1 + 1.1 < 2
1.2 < 2.
This works.
Since x=4.1 is a valid solution, eliminate any answer choice that does not include x=4.1 within its range.
Eliminate D and E.
C implies that x must be LESS than 4.5.
Test x=4.5.
If we plug x=4.5 into |x-4|+|x-3|<2, we get:
|4.5 - 4| + |4.5 - 3| < 2
0.5+ 1.5 < 2
2 < 2.
Doesn't work.
Since x=4.5 is NOT a valid solution, eliminate any answer choice that includes x=4.5 within its range.
Eliminate A and B.
The correct answer is
C.
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