Solve this problem

Question

Solve. 2.) | x + 1 | -2 =| 2x - 5 |

Answer 1

Consider x+1≥0 and 2x-5≥0, then x≥-1 and x≥5/2. Since 5/2>-1 we can consider when x≥5/2, then:

(x+1)-2=2x-5, x-1=2x-5, 4=x, so x=4 is one solution (4>5/2).

Now consider -1≤x≤5/2, then:

x+1-2=5-2x, x-1=5-2x, 3x=6, x=2 is another solution (2 is within the interval [-1,5/2]).

Finally consider x≤-1 then:

-x-1-2=5-2x, -x-3=5-2x, x=8, but this is not another solution because x cannot be both 8 and ≤-1.

Therefore the solutions are x=2 or 4.