Inequalities

[hpgmat]

which of the following inequalities is an algebric expression for the shaded part of the number line above? ( on the X axis , numbers in between and including -5 and 3 are shaded)

A) |X|≤ 3
B) |x| ≤ 5
C) |X-2| ≤ 3
D) |X-1| ≤ 4
E) |X+1| ≤ 4

i am debating between B and E. please give help with explanation.

[DanaJ]

B. |x| <=5 means that -5 <= x <=5. If that's the case, then this inequality also contains numbers that are beyond 3 (to the right of 3, actually). B is no good.

E. |x + 1| <=4
-4 <= x + 1 <=4 --- subtract 1
-5 <=x <=3 - here's the answer you're looking for.

[ankitns]

B. |x| <=5 means that -5 <= x <=5. If that's the case, then this inequality also contains numbers that are beyond 3 (to the right of 3, actually). B is no good.

E. |x + 1| <=4
-4 <= x + 1 <=4 --- subtract 1
-5 <=x <=3 - here's the answer you're looking for.

I get the same answer witht the same approach.

[hpgmat]

Thanks , now , i remember the trick for solving inequalities with absolute signs.

[real2008]

it is D

[pandeyvineet24]

Should be E as explained by DanaJ