-5--------------3
Which of the following inequalities is an algebraic
expression for the shaded part of the number line
above [including -5 and 3]?
a> |x| <=3
b> |x| <=5
c> |x-2| <=3
d> |x-1| <=4
e> |x+1| <=4
A very efficient approach would be to use POE (process of elimination).
Since x=-5 is part of the range, x=-5 must satisfy the inequality contained in the correct answer choice.
A quick scan of the answer choices shows that A, C and D can be eliminated:
A) |-5| ≤ 3. Doesn't work.
C) |-5-2| ≤ 3. Doesn't work.
D) |-5-1| ≤ 4. Doesn't work.
Answer choice B can be eliminated because |x| ≤ 5 includes x=5, which is not part of the given range.
The correct answer is
E.
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