Let's solve the absolute value equation step by step:
---
Problem:
$$
3 - |8x - 6| = 3
$$
---
Step 1: Isolate the absolute value expression
We want to get the absolute value term by itself on one side.
Subtract 3 from both sides:
$$
3 - |8x - 6| - 3 = 3 - 3
$$
$$
-|8x - 6| = 0
$$
Now, divide both sides by -1:
$$
|8x - 6| = 0
$$
---
Step 2: Solve the absolute value equation
The absolute value of a number is zero
only when the expression inside is zero. So:
$$
8x - 6 = 0
$$
Solve for $ x $:
$$
8x = 6
$$
$$
x = \frac{6}{8} = \frac{3}{4}
$$
---
✔ Final Answer:
$$
\boxed{x = \frac{3}{4}}
$$
---
Explanation:
- The equation $ |8x - 6| = 0 $ has
only one solution, because the absolute value is zero only when the inside is zero.
- There are
no other cases (like positive or negative) because absolute value equals zero only in one scenario.
- So, we don’t need to split into two equations here — just solve $ 8x - 6 = 0 $.
---
✔ Answer: $ \boxed{\frac{3}{4}} $
Let me know if you'd like to see a graph or check the solution!
Parent Tip: Review the logic above to help your child master the concept of solving absolute value equations worksheet algebra 2.
