If |x - 2| = |x + 3|, x could equal

Question

A. -5
B. -1/2
C. 1/2
D. 5
E. No real solution

ENGRTOMBA2018 · Accepted Answer

By definition, |x-a| = distance of x from a. In other words, |x-2| = distance of x from 2 and |x+3| = distance of x from -3.

Thus, if |x-2| = |x+3| ---> distance of x from 2 = distance of x from -3. Thus, x = halfway between -3 and 2.

Distance between -3 and 2 = 5 units. Thus x is 2.5 units away from 2 or -3 , giving you x = 2-2.5 or = -3+2.5 = -0.5,

B is thus the correct answer.

Divyadisha · Answer

is the answer 'B'

I back solved the question by putting answer choices in the question. -1/2 gives 5/2 on both sides.

Thanks

HKD1710 · Answer

|x - 2| = |x + 3|

We see both the sides are positive, hence we can square both the sides and we get

X^2 + 4 -4x = X^2 + 9 -6x

10x= -5

X= -1/2

Answer is B.

Razween · Answer

Since there are two Equations. Lets solve by Critical Value |x - 2| = |x + 3| Critical Value will be 2, -3 hence we Have 3 Solutions Solution No 1 When X < -3 ( RHS Will be Negative ) There fore x-2 = - (x + 3 ) => 2x = -1 => x = -1/2 which is not in line with x< -3 , hence rejected Solution No 2 When -3 < X <= 2 ( LHS will be Negative ) -(x-2) = x+3 => 2x= -1 => x = -1/2 which fits in the range Hence Solution. We can check by substituting in |x - 2| = |x + 3| Therefore 5/2= 5/2 Solution 3 when X > 2 both sides positive x-2 = x+3 No Value hence rejected

sudhirmadaan · Answer

Bunuel, in one of your post , you ave explained if we have mod on both side of the equation, we can safely square on both side 
(x-2)^2= (x+3)^2
by solving we get x= -1/2 . 
Please correct me if i missed something.

chetan2u · Answer

..

Hi sudhir,

yes, whenever you have ONLY mods on both sides..
example |a+b-2|>|a-b-4|... you can square both sides to fet your answer..
and you have correctly found your answer here

msk0657 · Answer

Given |x - 2| = |x + 3| The best way to get rid of the modulus is to square on both sides. (x - 2)^2 = (x+3)^2 => x^2 + 4 + 4x = x^2 + 9 + 6x => x = -1/2. Correct answer is B...

astroshagger · Answer

In the first condition in which X is less than -3, why isn't the (x-2) term negative as well? The expression (x-2) is negative for all values where X is less than 2.

Bunuel · Answer

Yes you are right.

If  x < -3 , then  |x - 2| = -(x - 2)  and  |x + 3| = -(x + 3) ;

If  -3 \leq x \leq 2 , then  |x - 2| = -(x - 2)  and  |x + 3| = x + 3 ;

If  x > 2 , then  |x - 2| = x - 2  and  |x + 3| = x + 3 .

generis · Answer

With absolute value equations this simple, for me, the method below is easy and fast (less than a minute).

The only way the two sides will be equal is if quantities inside the absolute value brackets are 1) equal or 2) equal but with opposite signs.

So |A| = B or -B*

1. Remove the absolute value bars

2. LHS = RHS or LHS = -RHS

3. Set up the two equations

Case 1: x - 2 = x + 3, OR

Case 2: x - 2 = -(x + 3)

4. Solve

Case 1: 
x - 2 = x + 3
-2 = 3. Not a solution

CASE 2: 
x - 2 = -(x + 3)
x - 2 = -x - 3
2x = -1
x = - \frac{1}{2}

5. Check x = - \frac{1}{2}  in equation. --> |- \frac{5}{2} | = | \frac{5}{2} |

Correct. x = - \frac{1}{2} .  Answer B

Hope it helps

* and |B| = A or -A. Technically there are four cases. Case 3 is RHS = LHS. Case 4 is RHS = - LHS. These two cases are identical to Cases 1 and 2.
Case 3: +RHS = +LHS, (x + 3) = (x - 2) (= Case 1)
Case 4: +RHS = -LHS, (x + 3) = (- x + 2). Multiply both sides by (-1) --> (-x - 3) = (x - 2) (= Case 2)

BrentGMATPrepNow · Answer

STRATEGY : As with all GMAT Problem Solving questions, we should immediately ask ourselves,   Can I use the answer choices to my advantage?   
In this case, we can easily test the answer choices. 
Now we should give ourselves about 20 seconds to identify a faster approach. 
In this case, we can also solve the equation. HOWEVER, since the equation involves  absolute values , we may end up solving two different equations (x - 2 = x + 3 as well as x - 2 = -(x + 3) before we arrive at the correct answer.
Given this, I think it may be faster to test the answer choices.

A. -5 
Plug in this value to get: |(-5) - 2| = |(-5) + 3|
Simplify: |-7| = |-2|
 Doesn't work.

B. -1/2 (aka -0.5) 
Plug in this value to get: |(-0.5) - 2| = |(-0.5) + 3|
Simplify: |-2.5| = |2.5|
  Works  !

Answer: B

BrushMyQuant · Answer

Given that |x - 2| = |x + 3| and we need to find the value of x

Let's solve this using three methods

Method 1: Substitution

Let's take values in each answer choice and substitutive in the equation and check which one satisfies the equation

A. -5 Put x = -5 in |x - 2| = |x + 3| and check if it satisfies the equation
=> |-5 - 2| = |-5 + 3| => |-8| = |-2|
=> 8 = 2 => FALSE

B. -1/2 Put x = -1/2 in |x - 2| = |x + 3| and check if it satisfies the equation
=> |-1/2 - 2| = |-1/2 + 3| => |-5/2| = |5/2|
=> 5/2 = 5/2 => TRUE

We don't need to check further as the question has asked for only one value

Method 2: Algebra

|x - 2| = |x + 3|
Square both the sides we get
\((|x-2|)^2 = (|x+3|)^2\)
=> \((x-2)^2 = (x+3)^2\)
=> \(x^2 -2*x*2 + 2^2 = x^2 + 2*x*3 + 3^2\)
=> \(x^2 -2*x*2 + 2^2 - x^2 - 2*x*3 - 3^2\) = 0
=> -4x + 4 - 6x - 9 = 0
=> -10x = 5
=> x = \(\frac{-5}{10}\) = \(\frac{-1}{2}\)

Method 3: Graphical Method

|x - 2| = Distance between x and 2
|x + 3| = | x - (-3)| = Distance between x and -3

Attachment:

-3 to 2.JPG [ 16.47 KiB | Viewed 6946 times ]

So, for Distance between x and 2 = Distance between x and -3
x has to be at the mid-point of -3 and 2
=> x = \(\frac{-3+2}{2}\) = \(\frac{-1}{2}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Absolute Value Problems

nisthagupta28 · Answer

If −3≤x≤2−3≤x≤2 , then |x−2|=−(x−2)|x−2|=−(x−2) and |x+3|=x+3|x+3|=x+3;
can you please help me understand it? because if we chose any value between -3 to 2 for x then |x-2| can be positive, negative, or 0. for example if we take X= -3 then |x-2| will be negative i.e. -x+2. but if we take x=2, then |x-2| will be 0.

do we then not consider the 0 case?

Paras96 · Answer

|x - 2| = |x + 3|, we will put the options as answers and then check for their correctness

A. -5=> |-7| = |-2| =>incorrect  
 B. -1/2 => |-5/2| =|5/2| => correct 
C. 1/2
D. 5
E. No real solution

Adit_ · Answer

Distance1=Distance2

first one is distance from 2
second is distance from -3
We need to find midpoint of these for distance to be equal.
2-3/2 = -1/2

Answer:  Option B

If |x - 2| = |x + 3|, x could equal

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If |x - 2| = |x + 3|, x could equal

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