Let's solve the equation step-by-step:

The equation is:

\[
\frac{1}{3}(6 + 3a) = 3a
\]

### Step 1: Distribute the \(\frac{1}{3}\) on the left side of the equation.

\[
\frac{1}{3} \times 6 + \frac{1}{3} \times 3a = 3a
\]

### Step 2: Simplify the terms.

\[
2 + a = 3a
\]

### Step 3: Move all the terms involving \(a\) to one side of the equation and constants to the other side.

\[
2 = 3a - a
\]

### Step 4: Combine like terms.

\[
2 = 2a
\]

### Step 5: Solve for \(a\).

\[
a = \frac{2}{2} = 1
\]

### Solution:

\[
a = 1
\]

Would you like more details or have any questions?

Here are some related questions you might consider:
1. How would the solution change if the equation was \(\frac{1}{4}(8 + 4a) = 4a\)?
2. What if the equation had an additional constant, such as \(\frac{1}{3}(6 + 3a) + 5 = 3a\)?
3. How would you solve for \(a\) if the equation was \(2(6 + 3a) = 6a\)?
4. What are the general steps to solve equations involving fractions?
5. How do you solve linear equations when the variable is on both sides?

**Tip:** When solving equations, always simplify expressions step-by-step and move all terms involving the variable to one side for easier calculation.

Learn how to solve the equation 1/3(6 + 3a) = 3a with a detailed step-by-step solution. This problem involves equations and fractions, covering how to simplify and solve equations with fractions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation