To solve the equation \( 30 + 5x = 38 + 7x \), let's follow these steps:

### 1. Move the variable terms to one side:
First, subtract \( 5x \) from both sides of the equation to get all the \( x \) terms on one side:
\[
30 = 38 + 7x - 5x
\]
Simplifying this, we get:
\[
30 = 38 + 2x
\]

### 2. Move the constant terms to the other side:
Next, subtract 38 from both sides to isolate the \( x \) term:
\[
30 - 38 = 2x
\]
Simplifying this, we get:
\[
-8 = 2x
\]

### 3. Solve for \( x \):
Now, divide both sides by 2 to solve for \( x \):
\[
x = \frac{-8}{2}
\]
\[
x = -4
\]

### Final Answer:
The solution is:
\[
\boxed{x = -4}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you check if a solution to a linear equation is correct?
2. What is the process for solving equations with variables on both sides?
3. How can you solve a linear equation with fractions?
4. What does it mean if a linear equation has no solution?
5. How would you solve \( 5x + 7 = 2x - 4 \)?

**Tip:** Always isolate the variable step by step, moving terms with the variable to one side and constants to the other.

Learn how to solve the linear equation 30 + 5x = 38 + 7x with a detailed step-by-step solution. This problem involves moving variable terms, isolating constants, and solving for x. Suitable for students in Grades 6-8.

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