The equation provided in the image is:

$5.4x + 12 = 2(2.7x - 9)$

Let's solve this step by step.

Step 1: Distribute the 2 on the right-hand side.

$5.4x + 12 = 2 \cdot 2.7x - 2 \cdot 9$ $5.4x + 12 = 5.4x - 18$

Step 2: Simplify both sides.

Now, let's move all terms involving $x$ to one side and the constants to the other:

$5.4x - 5.4x = -18 - 12$ $0 = -30$

Step 3: Conclusion

Since this results in $0 = -30$, which is a contradiction, this means there is no solution to the equation. This type of result indicates that the equation is inconsistent.

Let me know if you have any questions or need further details.

Here are some related questions to explore:

1. What does it mean when an equation has no solution?
2. Can you give an example of an equation that has infinitely many solutions?
3. How can you tell if a system of equations has no solution by graphing?
4. What is the difference between a contradiction and an identity in algebra?
5. How do you solve systems of linear equations using substitution or elimination?

Tip: Always check for contradictions when simplifying equations, as they can indicate that no solution exists.