The equation shown in the image is:

$0.5(x + 4) = 0.5x + 2$

Let's solve this equation step by step.

Step 1: Distribute the $0.5$ on the left-hand side

$0.5(x + 4) = 0.5x + 0.5 \times 4$ $0.5x + 2 = 0.5x + 2$

Step 2: Simplify the equation

The equation simplifies to: $0.5x + 2 = 0.5x + 2$

Step 3: Eliminate $0.5x$ from both sides

Subtract $0.5x$ from both sides: $0.5x + 2 - 0.5x = 0.5x + 2 - 0.5x$ $2 = 2$

This results in a true statement: $2 = 2$, which means that the equation is true for all values of $x$. Therefore, the solution is:

$\text{The equation has infinitely many solutions.}$

Would you like more details or have any questions about this?

Here are some related questions for further exploration:

1. What happens if you solve an equation that results in a contradiction like $3 = 5$?
2. How do you check for extraneous solutions when solving equations?
3. Can equations with variables on both sides have no solution? If so, when?
4. How do you solve quadratic equations if they arise from similar problems?
5. What are the different types of equations that always have infinite solutions?

Tip: Always verify your final result by plugging it back into the original equation to check if it holds true.