Question

20 POINTS PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve the equation. Check for extraneous solutions.

9∣9-8x∣ = 2x+3

Answer 1

Answer:

39/37 and 6/5

Step-by-step explanation:

To start, let's assume that 9-8x is positive (we will do this to get rid of the absolute value, but then check later). We get 9(9 - 8x) = 2x + 3, or 81 - 72x = 2x + 3, so 74x = 78 and x = 39/37. If we assume 9-8x is negative, the |9-8x| will turn into 8x-9, so we get 9(8x - 9) = 2x + 3, or 72x - 81 = 2x + 3 , so 70x = 84 and x = 6/5. If we plug the values back in, 9-8(39/37) needs to be positive, which works, and 9-8(6/5) needs to be negative, and this works, so the answers are 39/37 and 6/5.