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B
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45% (02:24) correct
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For all values of x between -2 and -1, what is the distance on the number line between 3x+4 and |x-1|?
A. 4x+3
B.-3-4x
C. 2x+5
D. 2x+3
E. 3x-3
A. 4x+3
B.-3-4x
C. 2x+5
D. 2x+3
E. 3x-3
09 Mar 2026, 01:58
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kevincan
Given that -2 < x < -1
Since we have a |x-1|, we need to find is the value of x inside mod - positive or negative.
subtract 1 in the initial equation, we get
-2 -1 < x-1 < -1-1
-3 < x-1 < -2
since (x-1) lies in the negative range. The x inside mod is negative.
so, |x-1| becomes - (x-1) = -x+1
Now, we have two values, (3x+4) and (-x+1)
Difference in distance = ?
Case 1: Difference in distance = (3x+4) - (-x+1) = 4x +3
Case 2: Difference in distance = (-x+1) - (3x+4) = -4x -3
we have two values, but the value of x should be within -2 and -1.
pick x = -1.5
case 1 = 4(-1.5)+3 = -3
case 2: -4(-1.5)-3 = 3
Distance is always positive. And ONLY CASE 2 Satisfies.
Answer is -4x-3
Option B
13 Mar 2026, 13:23
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I tried this way
just take any value between -2 & -1 say x=-3/2
for this value 3x+4=-1/2 and |x-1|=5/2 hence distance between them =3
now putting same value in the given options
1. 4x+3=-3
2. -3-4x=3
3. 2x+5=2
4. 2x+3=1
5. 3x-3=-7.5
can be checked with some other values or the given outliers, correct choice will be B.
just take any value between -2 & -1 say x=-3/2
for this value 3x+4=-1/2 and |x-1|=5/2 hence distance between them =3
now putting same value in the given options
1. 4x+3=-3
2. -3-4x=3
3. 2x+5=2
4. 2x+3=1
5. 3x-3=-7.5
can be checked with some other values or the given outliers, correct choice will be B.
