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kanusha
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For what value of x, is |x – 3| + |x + 1| + |x| = 10? 08 Jan 2017, 15:20
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Plug In options
A 3+1+ 0 NO
C 6 + 2 + 3 NO
D 1 + 5 + 4 = 10 Yes
D
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For what value of x, is |x – 3| + |x + 1| + |x| = 10? 20 Feb 2017, 02:15
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mun23
‘For how many values of x, is |x – 3| + 3|x + 1| + |x| = 4?’ The answer is 0. Why?
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I guess the test taker is asking for how many values equation is satisfied and it will be 2
which are -2 and -2/5
I am beginner Maths expert opinion is reliable
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For what value of x, is |x – 3| + |x + 1| + |x| = 10? 16 Dec 2024, 18:41
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KarishmaB
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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

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 = -8 (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.
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When checking for -1 < x < 0, shouldn't the term |x + 1| be positive and the term |x| be negative? Because if for example I take x= -0.5 and put that value in the mod terms, the mod term |x + 1| will be positive and |x| will be negative? Eventually x = -6 which does not satisfy the interval -1 < x < 0 .
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For what value of x, is |x – 3| + |x + 1| + |x| = 10? 10 Jan 2025, 13:14
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I am wondering if we can follow the wavy curve to realise that values of x above 3 will be positive and should grow bigger given the way this equation is set up. At 3, we have 7, so need to move to the right to get 10 and only answer choice > 3 is 4.
mun23
For what value of x, is |x – 3| + |x + 1| + |x| = 10?

(A) 0
(B) 3
(C) -3
(D) 4
(E) -2
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For what value of x, is |x – 3| + |x + 1| + |x| = 10? 08 Mar 2025, 07:14
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KarishmaB
carcass



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

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 = -8 (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.
Show more
In the case when -1 < x < 0 , this should be the answer:

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