The equation in the image is:

$|5x| + 5 = 45$

Steps to solve:

1. Isolate the absolute value: Subtract 5 from both sides: $|5x| = 45 - 5$ $|5x| = 40$

2. Solve the absolute value equation: This gives two possible cases because of the absolute value:

   • Case 1: $5x = 40$
   • Case 2: $5x = -40$

3. Solve each case:

   • For $5x = 40$: $x = \frac{40}{5} = 8$
   • For $5x = -40$: $x = \frac{-40}{5} = -8$

Final Answer:

$x = 8 \quad \text{or} \quad x = -8$

Let me know if you want more details or have any questions!

Here are some related questions to practice:

1. What is the general approach for solving absolute value equations?
2. How do you solve $|3x + 7| = 15$?
3. What happens if the right-hand side of an absolute value equation is negative?
4. How can absolute value functions be represented graphically?
5. How would the equation change if it were $|5x + 2| + 5 = 45$?

Tip: Always check for extraneous solutions when solving absolute value equations.