To solve the equation $8 + 2 |3 - x| = 8$, we can follow these steps:

1. Isolate the absolute value term: $8 + 2 |3 - x| = 8$ Subtract 8 from both sides: $2 |3 - x| = 0$

2. Divide by 2: $|3 - x| = 0$

3. Solve the absolute value equation: The only way for $|3 - x| = 0$ is if the expression inside the absolute value is zero: $3 - x = 0$ Solving for $x$: $x = 3$

Solution:

The solution to the equation is: $x = 3$

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Related Questions

1. How do we solve absolute value equations with two solutions?
2. What if the equation had been $8 + 2 |3 - x| = 10$?
3. Can absolute values result in negative solutions?
4. How would this equation change if $8 + 2 |3 - x| = 4$?
5. What are common applications of absolute value equations in real life?

Tip

Remember, an absolute value equation $|A| = B$ has no solution if $B < 0$ because absolute values cannot be negative.