Question

Solve the following equation. if there are multiple answers, enter each answer separated by a comma. enter none none​ if there are no solutions. − ∣ 15 − 18/x ∣ = − 17

A. x=−9
B. x= 9/16
C. None of the above
D. Both A and B

Answer 1

To solve the equation − ∣ 15 − 18/x ∣ = − 17, we remove the absolute value sign and solve for x in the resulting equations. The solutions are x = -9/16 and x = -9, so the correct answer is D. Both A and B.

Step-by-step explanation:

To solve the equation − ∣ 15 − 18/x ∣ = − 17, we can start by removing the absolute value sign. Since the equation is equal to a negative number, we know that the expression inside the absolute value must also be negative. This gives us two cases:

Case 1: 15 - 18/x = -17

Case 2: 15 - 18/x = 17

Simplifying each case, we get:

Case 1: -18/x = -32

Case 2: -18/x = 2

Now, we can solve for x in each case:

Case 1: x = -18/32 = -9/16

Case 2: x = -18/2 = -9

Therefore, the solutions to the equation are x = -9/16 and x = -9. So, the correct answer is D. Both A and B.