https://file.aiquickdraw.com/mathbot/file/1728323784426yfqypppd.jpg

The equation provided in the image is:

\[
-6x + 30 = -3x + 60
\]

### Let's solve the equation step by step:

1. Move all terms with \(x\) to one side and constant terms to the other. Start by adding \(6x\) to both sides to eliminate the \(-6x\) on the left:
   \[
   30 = 3x + 60
   \]

2. Now subtract 60 from both sides to move constants to the left side:
   \[
   30 - 60 = 3x
   \]
   \[
   -30 = 3x
   \]

3. Finally, divide both sides by 3 to solve for \(x\):
   \[
   x = \frac{-30}{3} = -10
   \]

### Therefore, the solution is \( x = -10 \).

The correct answer is **C**.

Would you like further details or have any other questions?

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Here are 5 related questions to explore this topic further:
1. How do you solve equations with variables on both sides?
2. What happens if the constants are on both sides of the equation?
3. How can we check if the solution for \(x\) is correct?
4. How do you solve equations with fractions or decimals?
5. How would this change if the equation had more complex terms (like exponents)?

**Tip:** Always double-check your solution by substituting the value of \(x\) back into the original equation to verify both sides are equal.

Learn how to solve the linear equation -6x + 30 = -3x + 60 using the balancing method. This problem covers key algebraic concepts and properties of equality. Suitable for students in Grades 7-9.

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