Let's solve the equation \( \frac{x}{3} + 7 = 2x \):

### Step 1: Eliminate the fraction
Multiply every term in the equation by 3 to get rid of the fraction:
\[
3 \times \left( \frac{x}{3} \right) + 3 \times 7 = 3 \times 2x
\]
This simplifies to:
\[
x + 21 = 6x
\]

### Step 2: Rearrange the equation
Move all terms involving \(x\) to one side by subtracting \(x\) from both sides:
\[
21 = 6x - x
\]
\[
21 = 5x
\]

### Step 3: Solve for \(x\)
Divide both sides by 5:
\[
x = \frac{21}{5}
\]

So, the solution is \(x = \frac{21}{5}\), or as a decimal, \(x = 4.2\).

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How do you solve equations with variables on both sides?
2. What if there were a different fraction, like \( \frac{x}{4} + 7 = 2x \)?
3. How would this change if the equation was \( \frac{x}{3} + 7 = 3x \)?
4. What is the process for solving quadratic equations?
5. How do you deal with equations that have fractions on both sides?

**Tip:** Always check your solution by plugging it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation x/3 + 7 = 2x step-by-step. This solution covers key algebraic concepts like eliminating fractions and isolating variables. Suitable for students in Grades 6-8.

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