Find the solution set for the equation.
-|r + 9| = 7
A) {16, -2}
B) {-16, -2}
C) {2}

Question

Find the solution set for the equation.
-|r + 9| = 7
A) {16, -2} 
B) {-16, -2} 
C) {2}

Quizplus · Accepted Answer

We can solve the equation by splitting it into two cases - one where r+9 is positive and one where r+9 is negative.

Case 1: r+9 is positive
In this case, the absolute value of r+9 will equal r+9. So we have:
r+9 = 7
Subtracting 9 from both sides gives us:
r = -2

Case 2: r+9 is negative
In this case, the absolute value of r+9 will equal -(r+9) or -r-9. So we have:
-r-9 = 7
Adding 9 to both sides gives us:
-r = 16
Multiplying both sides by -1 (or dividing by -1, since we are solving for r) gives us:
r = -16

So the solution set for the equation is {-16, -2}, which corresponds to choice B. To solve the equation |r + 9| = 7, we need to split it into two separate equations:
r + 9 = 7 or r + 9 = -7
Solving for r in the first equation, we get r = -2.
Solving for r in the second equation, we get r = -16.
Therefore, the solution set is {-16, -2}, which is choice B.

Find the Solution Set for the Equation