Solve the given linear equation.
3x + 4 = 8x − 42

To solve the linear equation \( 3x + 4 = 8x - 42 \), follow these steps:

### Step 1: Move all the terms involving \(x\) to one side of the equation.
Subtract \(3x\) from both sides:
\[
4 = 8x - 3x - 42
\]
Simplifying this gives:
\[
4 = 5x - 42
\]

### Step 2: Move constant terms to the other side.
Add \(42\) to both sides:
\[
4 + 42 = 5x
\]
\[
46 = 5x
\]

### Step 3: Solve for \(x\).
Now, divide both sides by \(5\):
\[
x = \frac{46}{5}
\]
\[
x = 9.2
\]

So, the solution to the equation is \( x = 9.2 \).

Do you want more details or have any questions?

Here are 5 related questions:
1. What is the general method to solve linear equations?
2. How do you check if the solution of a linear equation is correct?
3. What is the difference between a linear and a quadratic equation?
4. How would you graph this linear equation on a coordinate plane?
5. Can linear equations have more than one solution?

**Tip:** Always simplify the equation step by step, keeping variables on one side and constants on the other.

Solve the given linear equation. 3x + 4 = 8x − 42

Learn how to solve the linear equation 3x + 4 = 8x − 42 with step-by-step instructions. This problem covers key algebraic concepts and demonstrates how to isolate the variable x. Suitable for students in Grades 6-8.

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