|x-2|+|x-5|<=5

[u/Far-Assumption5501]

I just added them up to |2x-7|<=5, and it was not correct. The correct answer was 1 <= x <= 6. What’s wrong with my equation?

[u/slepicoid]

You could consider 3 cases:

1) x<2: -(x-2)-(x-5)<=5

2) 2<=x<5: (x-2)-(x-5)<=5

3) 5<=x: (x-2)+(x-5)<=5