Question

If possible, solve each equation or inequality.

1.) lxl= -2
2.) l x+9 l >11
3.) x^2 - 2= 14
4.) (x-7)^2 = 169
5.) x^2-2=14
6.) x^2= -2.56

Answer 1

First one is not solvable, as the modulus of x is always positive.

Or you can square both sides of it to get \[x^2 + 18x + 81 < 121\]\[x^2 + 18x -40 <0\]\[(x+20)(x-2)<0\] Now you need to envisage this on a graph, so the shaded region, is the bit that is less than 0 (as the equation requires. So your solution here is \[-20<x<2\]