For what value of x, is |x – 3| + |x + 1| + |x| = 10?

Question

(A) 0
(B) 3
(C) -3
(D) 4
(E) -2

KarishmaB · Accepted Answer

Going the algebra way, you have missed two cases. There are 3 transition points: -1, 0, 3

When x > 3, 
 |x - 3| + |x + 1| + |x| = 10 
 x - 3 + x + 1 + x = 10 
x = 4
Satisfies

When 0 < x < 3
 |x - 3| + |x + 1| + |x| = 10 
 -(x - 3) + (x + 1) + x = 10 
x = 6 (Not possible since 0 < x < 3)

When -1 < x < 0
 |x - 3| + |x + 1| + |x| = 10 
 -(x - 3) + (x + 1) - x = 10 
x = -6 (Not possible since -1 < x < 0)

When x < -1
 |x - 3| + |x + 1| + |x| = 10 
-(x - 3) - (x+1) - x = 10
x = -8/3 
Satisfies

Better is the number line method.

The question has been picked from here. Mind you, I have discussed two different questions:
1. For what value of x, is |x – 3| + |x + 1| + |x| = 10?
2. For how many values of x, is |x – 3| + |x + 1| + |x| = 10?

The method to be used is different in the two cases. As Ron mentioned above, just plug in the options in the first question. In the second question, you can use the number line to quickly solve it. Check out the post to avoid confusion.

*Edited

JimGMATAnswers · Answer

This should define x as and integer. I would be careful with your sources...

VeritasPrepRon · Answer

Often on these types of questions you're better off just plugging in answer choices and seeing which one is correct. Once you plug in 3 and get (3-3) + (3+1) + 3 = 7, you can figure out that if you added one more to X, you'd get a new answer that's 3 higher than your old answer. However, even if you don't overthink anything and just plug the choices in in succession, you still get the right answer in well under 2 minutes. If you're struggling with these types of questions, keep it simple and you'll be fine.

Hope this helps!
-Ron

Carcass · Answer

Here you can:

a) test each answer choice OR
b) take the algebra way

Both are fast but it depends how you are comfortable but if you start thinking about the positive side of absolute value --->  x - 3 + x + 1 + x = 10  --->  3x = 12 x = 4   OR  - x + 3 -x - 1 - x = 10  ---->  - 3x = 8  NOT POSSIBLE

Only D takes in account. in no more than 50 seconds - 60 at maximum

regards

KarishmaB · Answer

There is no reason to define x as an integer. 
There is no value of x which satisfies this equation - integer or real number.

mun23 · Answer

Hi karisma
Whats the difference between for what value of x &for how many values of x.........

KarishmaB · Answer

'For what value of x....' implies you are looking for one particular value of x. There could be 2 or more values satisfying this equation but you are looking for only one - the one which is included in your options.

x can take two values here: 4 and -8/3

'For what value of x....' will be answered by 4. 4 is one of the values that satisfy this equation. The other one, -8/3, is not in the options which is logical since only one option can be correct. This question is generally simpler since you can plug in the options to see which value satisfies the equation.

'For how many values of x ...' means 'how many values can x take?' The answer here will be 2. x can take 2 values: 4 and -8/3. This question is usually more complex. You need to find the number of values x can take. The options will be something like: 0, 1, 2, 3, 'More than 3'. Here, you cannot plug in the options since the options do not give you the values x can take. They only give you the number of values. So you actually need to solve the equation to get how many values x can take.

Dwija01 · Answer

KarishmaB

I got
-1<x<0 as
-(x+3)+(x+1)-(x)=10
-x-3+x+1-x=10
4-x=10
x=-6

Plz explain how you assumed the signs for this one.

KarishmaB · Answer

You are right. |x+1| will be positive and |x| will be negative. Edited.

For what value of x, is |x – 3| + |x + 1| + |x| = 10?

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For what value of x, is |x – 3| + |x + 1| + |x| = 10?

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