We are given the equation:

\[
-38 + 6x = -12x + 52
\]

To solve for \( x \), follow these steps:

### Step 1: Combine like terms
Move all the terms with \( x \) to one side and constant terms to the other side. First, add \( 12x \) to both sides:

\[
-38 + 6x + 12x = 52
\]

\[
-38 + 18x = 52
\]

### Step 2: Isolate the \( x \)-term
Next, add 38 to both sides to move the constant term to the other side:

\[
18x = 52 + 38
\]

\[
18x = 90
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 18 to solve for \( x \):

\[
x = \frac{90}{18}
\]

\[
x = 5
\]

Thus, the solution is:

\[
x = 5
\]

Would you like more details or further explanation?

### Related Questions:
1. How do you solve linear equations with variables on both sides?
2. Can linear equations have more than one solution?
3. How do you handle equations with fractions?
4. What are some methods for checking the solution of an equation?
5. How can you solve an equation involving parentheses?

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

Learn how to solve the linear equation -38 + 6x = -12x + 52 with a step-by-step solution. This problem involves combining like terms, isolating the variable, and dividing to solve for x. Suitable for students in Grades 7-8.

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