Please solve: -2|x - 3| - 1 < -7?

| x - 3 | < (-6) / (-2)

| x - 3 | < 3

- 3 < x - 3 < 3

0 < x < 6

-2|x - 3| - 1 < -7

Add 1 to each side:

-2|x - 3| < -6

Divide both sides by -2. (Since we are dividing by a negative number, this flips the inequality sign):

|x - 3| > 3

This inequality says that the distance between x and 3 is more than 3 units, which means

either x > 6 or x < 0.

So the solution set is {x | x < 0 or x > 6}, which can be written in interval notation as (-∞, 0) U (6, ∞).

-2|x - 3| - 1 < -7
-2|x - 3| < -7 + 1
-2|x - 3| < -6
|x - 3| > -6/-2
|x - 3| > 3
x - 3 > 3 , x - 3 < -3

x - 3 > 3
x > 3 + 3
x > 6

x - 3 < -3
x < -3 + 3
x < 0

∴ x > 6 , x < 0

-2/x-3/-1 < -7
-2/x-3/ -1 +1 < -7+1
-2/x-3/ < -6
2/x-3/ < 6
/x-3/ < 3
-3 < x-3 < 3
-3+3 < x-3+3 < 3+3
0<x<6
Hope it helps