# The 2 absolute equation equality? find the max and min of x?

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1. Jun 20, 2017

### Helly123

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
2x - 1 >= 0
x >= 1/2

x - 2 >= 0
x >= 2

for x <1/2
then 2x - 1 and x - 2 are negative
solve : -(2x-1) - (x-2) = 2
-3x + 3 = 2
x = 1/3

for 1/2 <= x < 2
the (2x - 1) positive, (x-2) negative
solve : 2x -1 -x + 2 = 2
x = 1

for x>= 2
both 2x -1 and x -2 = positive
2x - 1 + x - 2 = 2
3x = 5
x = 5/3

is my answer right? then the max of x is 5/3? and the min is 1/3?

2. Jun 20, 2017

### Staff: Mentor

These are the values I get, as well.

3. Jun 20, 2017

### Helly123

so what's the max and min of x? because the key answer not 1/3 and 5/3. but 1/3 and 1

4. Jun 20, 2017

### mjc123

Your third case is self-contradictory. On the assumption that x >= 2, you get x = 5/3, which is < 2. So this case is ruled out, and the answers are 1/3 and 1.

5. Jun 20, 2017

### Staff: Mentor

Yes, @mjc123 is correct. I wasn't careful enough in checking my solutions. The maximum value is x = 1.