Problem Solving

I don't get this. I see 2 correct answers. Please help:

Number Line of x:

Number line is from -5 to 5. Numbers -5 <through> 3 are shaded.

130. Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

<= is "less than or equal to"

B and E seem correct to me. Book has it as E being correct.
Isn't |-5| = 5 which is <=5.

The thing that the GMAT does is funny , the hard part of the question is not answering it but understanding it , I struggle just like you buddy , hope this helps .

no.130 OG 11th edition PS

x can = -5 however since the minimum value of x is -5 lx+1l can never be -5 because then -6 + 1 = -5

thats why its E

The thing that the GMAT does is funny , the hard part of the question is not answering it but understanding it , I struggle just like you buddy , hope this helps .

no.130 OG 11th edition PS

x can = -5 however since the minimum value of x is -5 lx+1l can never be -5 because then -6 + 1 = -5

thats why its E

You've answered this yourself.

The number line is highlighted from -5 to 3 (inclusive). For B, the equation is TRUE if x = 5; however, 5 is not highlighted on the number line, so it is clearly not the answer.

When working with absolute values, do this following:

|x - 3| <= 1 means

-1 <= (x - 3) <= 1 which means

2 <= x <= 4

Just learn and follow the above pattern, and you'll solve it.

detonate wrote:I don't get this. I see 2 correct answers. Please help:

Number Line of x:

Number line is from -5 to 5. Numbers -5 <through> 3 are shaded.

130. Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

<= is "less than or equal to"

B and E seem correct to me. Book has it as E being correct.
Isn't |-5| = 5 which is <=5.

detonate wrote:I don't get this. I see 2 correct answers. Please help:

Number Line of x:

Number line is from -5 to 5. Numbers -5 <through> 3 are shaded.

130. Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

<= is "less than or equal to"

B and E seem correct to me. Book has it as E being correct.
Isn't |-5| = 5 which is <=5.

Put the max/min true values from number line and get the answer.
Options:
(A) |x|<= 3 ---max---> 3 On shaded part ---min---> -5 Do not satisfy the equation Eliminate
(B) |x|<= 5 ---max---> 5 Not on shaded part Eliminate
(C) |x-2|<= 3 ---max---> 5 Not on shaded part Eliminate
(D) |x-1| <= 4 ---max---> 5 Not on shaded part Eliminate
(E) |x+1| <= 4 ---max---> 3 On shaded part ---min---> -5 On shaded part ANSWER

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

A) |x| <= 3
B) |x| <= 5
C) |x-2| <= 3
D) |x-1| <= 4
E) |x+1| <= 4

|x-y| = the DISTANCE between x and y

The midpoint of the range = -1.
x can be any value from -5 (4 places BELOW -1) to 3 (4 places ABOVE -1).
In other words: the distance between x and -1 is less than or equal to 4.
In math terms:
|x-(-1)| ≤ 4.
|x+1| ≤ 4.

The correct answer is E.

An alternate approach is to plug numbers into the answer choices.
The correct answer choice must work for EVERY value between -5 and 3, inclusive -- and for no values outside this range.
Since |x| = the distance between x and 0, start with the value furthest from 0:
Let x=-5.
Eliminate any answer choice in which x=-5 doesn't work.

Answer choice A: |x|≤3
|-5|≤3.
5≤3.
Doesn't work. Eliminate A.

Answer choice B: |x|≤5
|-5|≤5
5≤5.
This works. Hold onto B.

Answer choice C: |x-2|≤3
|-5-2|≤3
7≤3.
Doesn't work. Eliminate C.

Answer choice D: |x-1|≤4
|-5-1|≤4
6≤4.
Doesn't work. Eliminate D.

Answer choice E: |x+1|≤4
|-5+1|≤4
4≤4.
This works. Hold onto E.

Only B and E remain.
Answer choice B -- |x|≤5 -- includes every value from -5 to 5, but the needed range is only from -5 to 3.
Eliminate B.

The correct answer is E.