Which of the following inequalities is equivalent to -3

Question

Which of the following inequalities is equivalent to -3 \leq x\leq{1} ? A. |x|\leq{1} B. |x|\leq{3} C. 1\leq{|x|}\leq{3} D. |x+1|\leq{2} E. |x-1|\leq{2} Exercise 1.png

Bunuel · Accepted Answer

A.  |x|\leq{1}

The above is equivalent to  -1 \leq x \leq 1

B.  |x|\leq{3}

The above is equivalent to  -3 \leq x \leq 3

C.  1\leq{|x|}\leq{3}

The above is equivalent to  1 \leq x \leq 3  or  -3 \leq x \leq -1

D.  |x+1|\leq{2}

The above is equivalent to  -2 \leq x + 1 \leq 2 , which yields  -3 \leq x  \leq 1 .

E.  |x-1|\leq{2}

The above is equivalent to  -2 \leq x - 1 \leq 2 , which yields  -1 \leq x  \leq 3 .

Answer: D.

gmatophobia · Answer

We start by eliminating the options

A.  |x|\leq{1}

-1 \leq x \leq 1

Eliminate .

B.  |x|\leq{3}

-3 \leq x \leq 3

Eliminate

Let's move to D first

D.  |x+1|\leq{2}

-2 \leq x + 1 \leq 2

Subtracting 1 on both sides

-2 - 1 \leq x \leq 2 -1

-3 \leq x \leq 1

This matches the expression given above.

Option D

MartyMurray · Answer

Which of the following inequalities is equi1 abvalent to   -3 \leq x\leq{1} ?

Fined the midpoint between   -3  and  1 .

\frac{- 3 + 1}{2} = -1

Find the distance between each endpoint and the midpoint.

|-3 - (-1)| = |1 - (-1)| = 2

So,   -3 \leq x\leq{1}  is equivalent to  |x - (-1)|\leq{2} .

A.  |x|\leq{1} 
B.  |x|\leq{3} 
C.  1\leq{|x|}\leq{3} 
D.  |x+1|\leq{2} 
E.  |x-1|\leq{2}

Correct answer:  D

lavanya.18 · Answer

I got the answer, but I had a little query regarding option C, how did we get  -3 \leq x \leq -1 ?

Bunuel · Answer

For option C,  1 \leq |x| \leq 3  gives two cases:

1 \leq x \leq 3  for positive x 
  1 \leq -x \leq 3  for negative x, which when multiplied by -1 gives  -3 \leq x \leq -1 . Notice that any x from this range satisfies  1 \leq |x| \leq 3 .

unraveled · Answer

Which of the following inequalities is equivalent to \( -3 \leq x\leq{1}\)?

A. \(|x|\leq{1}\)
x < 0 gives x >= -1
x > 0 gives x<= 1

So, it's only a part of the required inequality. Eliminate

B. \(|x|\leq{3}\)
Going by above logic that we applied in A, this too has to be eliminate. This actually covers a bigger range as the required inequality covers.

C. \(1\leq{|x|}\leq{3}\)
x = 0 is not true. So, eliminate.

D. \(|x+1|\leq{2}\)
x < 0 gives x >= -3
x > 0 gives x <= 1

This is the answer.

E. \(|x-1|\leq{2}\)
x < 0 gives x >= -1
x > 0 gives x <= 3
Like A, eliminate.

Answer D.

DanTheGMATMan · Answer

Best just to see which answer choice gives you the exact inequality:
 https://www.youtube.com/watch?v=lXbErHeCQNo

GmatKnightTutor · Answer

Which of the following inequalities is equivalent to   -3 \leq x\leq{1} ?

A.  |x|\leq{1} 
B.  |x|\leq{3} 
C.  1\leq{|x|}\leq{3} 
D.  |x+1|\leq{2} 
E.  |x-1|\leq{2}

Add 1 to the expression.

-3 + 1 \leq x + 1\leq{1 + 1}

-2 \leq x + 1\leq{2}

|x + 1|\leq{2}

(D) is your answer.

Which of the following inequalities is equivalent to -3 <= x <= 1

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