Can somebody please help me with solving this and show steps if they can. Solve the equation. Check for extraneous solutions. 9|9-8X|=2X+3

For my answer I got X=-1
I divided by 9 on both sides I got 8X=2X-6
Then I divided by 6 on both sides and got X=-1

Your correct GOOD JOB

not even close. See other post(s) on this problem.

To solve the equation |9-8X| = 2X + 3 and check for extraneous solutions, you followed the correct steps up to a point, but there was an error in the subsequent step.

Here's a step-by-step explanation of how to solve the equation, including how to avoid making mistakes:

1. Start with the equation |9-8X| = 2X + 3.

2. Split the equation into two cases based on the absolute value:
a) 9 - 8X = 2X + 3
b) 9 - 8X = -(2X + 3)

3. Solve case (a):
Simplify the equation: 9 - 8X = 2X + 3
Subtract 2X from both sides: 9 - 10X = 3
Subtract 9 from both sides: -10X = -6
Divide both sides by -10: X = 0.6

4. Solve case (b):
Simplify the equation: 9 - 8X = -(2X + 3)
Distribute the negative sign: 9 - 8X = -2X - 3
Add 8X to both sides: 9 = 6X - 3
Add 3 to both sides: 12 = 6X
Divide both sides by 6: X = 2

5. The two potential solutions are X = 0.6 and X = 2.

6. Check for extraneous solutions by substituting each solution back into the original equation and verifying if the left side equals the right side:
For X = 0.6: |9 - 8(0.6)| = 2(0.6) + 3 => |9 - 4.8| = 1.2 + 3 => |4.2| = 4.2 + 3 => 4.2 = 7.2
Since 4.2 is not equal to 7.2, X = 0.6 is not a valid solution.

For X = 2: |9 - 8(2)| = 2(2) + 3 => |9 - 16| = 4 + 3 => |-7| = 7 => 7 = 7
Since 7 is equal to 7, X = 2 is a valid solution.

7. Therefore, the solution to the equation |9-8X|=2X+3 is X = 2.