Let's solve the equation \( 4x + 34 = 6x - 20 \).

### Step 1: Move all terms involving \( x \) to one side.
Subtract \( 4x \) from both sides:

\[
4x + 34 - 4x = 6x - 20 - 4x
\]
\[
34 = 2x - 20
\]

### Step 2: Move the constant terms to the other side.
Add 20 to both sides:

\[
34 + 20 = 2x - 20 + 20
\]
\[
54 = 2x
\]

### Step 3: Solve for \( x \).
Divide both sides by 2:

\[
x = \frac{54}{2} = 27
\]

So, the solution is \( x = 27 \).

Do you want further details or have any questions?

Here are 5 related questions:
1. How do you solve an equation with variables on both sides?
2. What happens if an equation has no solution?
3. How would you solve \( 5x - 3 = 3x + 7 \)?
4. What is the difference between an equation and an inequality?
5. How do you check if your solution to an equation is correct?

**Tip:** Always check your solution by plugging the value of \( x \) back into the original equation!

Learn how to solve the linear equation 4x + 34 = 6x - 20 with a detailed step-by-step solution. This guide covers essential algebraic concepts, including moving variables to one side and isolating x. Suitable for students in Grades 6-8.

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