|x - 8|- 15 = -6
How do I solve this.. Please don't do it for me..
Two problems:
1. x-8 -15 = -6
2. -x+8 -15 = -6
Or, you can say that if
|x| = 4
x = ±4
so, if
|x-8|-15 = -6
|x-8| = 9
x-8 = ±9
...
To solve the equation |x - 8| - 15 = -6, you can follow these steps:
Step 1: Isolate the absolute value term
Add 15 to both sides of the equation:
|x - 8| = -6 + 15
|x - 8| = 9
Step 2: Split the equation into two cases
|x - 8| = 9 could mean either (x - 8) = 9 or (x - 8) = -9. This is because the absolute value of a number can equal the positive or negative value.
Case 1: (x - 8) = 9
Solve for x by adding 8 to both sides:
x - 8 = 9 + 8
x - 8 = 17
Add 8 to both sides to isolate x:
x = 17 + 8
x = 25
Case 2: (x - 8) = -9
Solve for x by adding 8 to both sides:
x - 8 = -9 + 8
x - 8 = -1
Add 8 to both sides to isolate x:
x = -1 + 8
x = 7
So, the equation |x - 8| - 15 = -6 has two possible solutions, x = 25 and x = 7.