Please help!
|x+1|-3 > 8
Solve the absolute value inequalities.
Please and thanks.
To solve the absolute value inequality |x+1|-3 > 8, we need to perform the following steps:
Step 1: Separate the inequality into two cases:
Case 1: If x+1 ≥ 0
In this case, the inequality becomes (x+1) - 3 > 8.
Case 2: If x+1 < 0
In this case, the inequality becomes -(x+1) - 3 > 8.
Step 2: Solve each case separately.
Case 1:
(x+1) - 3 > 8
x + 1 - 3 > 8
x - 2 > 8
x > 10
Case 2:
-(x+1) - 3 > 8
-x - 1 - 3 > 8
-x - 4 > 8
-x > 12 (multiplying both sides by -1)
x < -12 (reversing the inequality)
Step 3: Combine the solutions from both cases.
The solutions for the absolute value inequality |x+1|-3 > 8 are x > 10 or x < -12.
Please note that when solving absolute value inequalities, the solution is provided as a combination of multiple cases. Each case is determined by the sign of the expression within the absolute value brackets (i.e., whether it is positive or negative), and the inequalities are solved accordingly for each case.