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# help

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91
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Solve |x - 2| + |x - 4| + |x + 3| = 10.

May 19, 2020

#1
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i dont know but i just realized thats an absolute value or did u mean brackets?

May 19, 2020
#2
0

oh dude, i got the answer!

May 19, 2020
#3
+93
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Yes, that is right but you used a calculator, which they could easily find

#6
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well dude, at least i got him the answer in only 2 mins not like yall take forever!

Guest May 19, 2020
#4
+21953
+1

I have a slightly different answer ....  |x - 2| + |x + 4| + |x + 3|  =  10

Remember that if the quantity within the abolute value bars is positive, just remove the

bars; but, if what is inside, you need to rewrite the expression as:  - (  expression  ).

There are 8 cases:

1) (+,+,+)  x - 2 >= 0   --->   x >= 2

x - 4 >= 0   --->   x >= 4

x + 3 >= 0   --->   x >= -3

< This is possible for x >= 4 >

|x - 2| + |x + 4| + |x + 3|  =  10     --->     (x - 2) + (x - 4) + (x + 3)  =  10

3x - 3  =  10

3x  =  13

This answer works because x >= 4:                                         x  =  13/3

2) (+, +, -)  x - 2 >= 0   --->   x >= 2

x - 4 >= 0   --->   x >= 4

x + 3 <= 0   --->   x <= -3

< This is impossible because x can't both be greater than 4 and less that -3 >

3) (+,-,+)   x - 2 >= 0   --->   x >= 2

x - 4 <= 0   --->   x <= 4

x + 3 >= 0   --->   x >= -3

< This is possible only for x >= 2 and x <= 4 >

|x - 2| + |x + 4| + |x + 3|  =  10     --->     (x - 2) - (x - 4) + (x + 3)  =  10

x + 5  =  10

This answer doesn't work because it isn't between 2 and 4:  x  =  5

4) (+,-,-)    x - 2 >= 0   --->   x >= 2

x - 4 <= 0   --->   x <= 4

x + 3 <= 0   --->   x <= -3

< This is impossible because x can't be both >= 2 and <= -3 >

5) (-, +, +)  x - 2 <= 0   --->   x <= 2

x - 4 >= 0   --->   x >= 4

x + 3 >= 0   --->   x >= -3

< This is impossible because x can't be both <= 2 and >= 4 >

6) (-,+,-)    x - 2 <= 0   --->   x <= 2

x - 4 >= 0   --->   x >= 4

x + 3 <= 0   --->   x ><-3

< This is impossible because x can't be both >= 4 and <= 2 >

7)  (-,-,+)   x - 2 <= 0   --->   x <= 2

x - 4 <= 0   --->   x <= 4

x + 3 >= 0   --->   x >= -3

< This is possible only for x >= -3 and x <= 2 >

|x - 2| + |x + 4| + |x + 3|  =  10     --->     - (x - 2) - (x - 4) + (x + 3)  =  10

-x + 9  =  10

- x  =  1

This answer works because it is between -3 and 2                  x  =  -1

8) (-,-,-)   x - 2 <= 0   --->   x <= 2

x - 4 <= 0   --->   x <= 4

x + 3 <= 0   --->  x <= -3

< This is possible only for x <= -3>

|x - 2| + |x + 4| + |x + 3|  =  10     --->     - (x - 2) - (x - 4) - (x + 3)  =  10

-3x + 3  =  10

- 3x  =  7

This answer doesn't work because it isn't <= -3                        x  =  -7/3

There are two answers::  -1  and  13/3

May 19, 2020
#5
+93
0

You are right, that does work out.