Explanation:
To solve for r in the absolute value equation:
|-8r - 6| = 9
We can split the equation into two cases, one where the expression inside the absolute value is positive and one where it is negative:
Case 1: -8r - 6 = 9
In this case, we remove the absolute value and solve for r:
-8r - 6 = 9
Add 6 to both sides:
-8r = 15
Divide both sides by -8:
r = -15/8
Case 2: -(-8r - 6) = 9
In this case, we change the sign inside the absolute value and solve for r:
8r + 6 = 9
Subtract 6 from both sides:
8r = 3
Divide both sides by 8:
r = 3/8
Therefore, the solutions for r in the absolute value equation are r = -15/8 and r = 3/8.