The equation shown in the image is:

$|-5x + 8| = |2x - 2|$

To solve this absolute value equation, we'll consider the cases where the expressions inside the absolute values are either equal or their negatives are equal.

Case 1:

$-5x + 8 = 2x - 2$

Solve for $x$:

Add $5x$ to both sides:

$8 = 7x - 2$

Add 2 to both sides:

$10 = 7x$

Divide by 7:

$x = \frac{10}{7}$

Case 2:

$-5x + 8 = -(2x - 2)$

Simplify the right-hand side:

$-5x + 8 = -2x + 2$

Solve for $x$:

Add $5x$ to both sides:

$8 = 3x + 2$

Subtract 2 from both sides:

$6 = 3x$

Divide by 3:

$x = 2$

Solutions

The solutions to the equation are $x = \frac{10}{7}$ and $x = 2$.

Would you like more details on these steps or have any further questions?

Here are some related questions for practice:

1. How would you solve an absolute value equation with three terms, such as $|ax + b| + |cx + d| = |ex + f|$?
2. What happens when the expressions inside the absolute values are more complex, like quadratic expressions?
3. How do you solve an absolute value inequality, such as $|ax + b| < c$?
4. What are the key differences between solving absolute value equations and inequalities?
5. How would you graph the equation $|-5x + 8| = |2x - 2|$?

Tip: When solving absolute value equations, always remember to check your solutions in the original equation, as extraneous solutions can sometimes appear.