I have to solve for x >>> l x - 3 l > 8
-(x-3)>8 or (x-3)>8
-x + 3 >8 or +x -3 >8
-x >5 or +x>11
x <-5 or x > 11
=================
check
if x = -6
l -6 - 3 l > 8
9 > 8 yes
if x = 12
l 12 - 3 l > 8
9>8 yess
Wait, where did you get -6 and 12 from to check?
I picked numbers just outside the allowed range.
|x - 3| > 8.
x - 3 > +- 8,
x > (+-8) + 3,
X > 11.
X > -5.
To solve for x in the inequality |x - 3| > 8, we need to consider two cases:
Case 1: x - 3 > 8
In this case, we isolate x to find the solution:
x > 8 + 3
x > 11
Case 2: -(x - 3) > 8
To solve this, we multiply both sides of the inequality by -1 and reverse the inequality sign:
x - 3 < -8
Next, add 3 to both sides of the inequality to isolate x:
x < -8 + 3
x < -5
Therefore, the solution to the inequality |x - 3| > 8 is x > 11 or x < -5.