To solve the equation:

\[
\frac{5}{3}z + 1 = 3 - \frac{2}{3}z
\]

Let's follow these steps:

### Step 1: Clear the Fractions

To eliminate the fractions, multiply every term by 3:

\[
3 \cdot \frac{5}{3}z + 3 \cdot 1 = 3 \cdot 3 - 3 \cdot \frac{2}{3}z
\]

This simplifies to:

\[
5z + 3 = 9 - 2z
\]

### Step 2: Combine Like Terms

Add \(2z\) to both sides to get all the \(z\) terms on one side:

\[
5z + 2z + 3 = 9
\]

This simplifies to:

\[
7z + 3 = 9
\]

### Step 3: Isolate the \(z\) term

Subtract 3 from both sides:

\[
7z = 6
\]

### Step 4: Solve for \(z\)

Divide both sides by 7:

\[
z = \frac{6}{7}
\]

### Solution

The solution to the equation is:

\[
\boxed{z = \frac{6}{7}}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you solve equations with variables on both sides?
2. What are the steps to clear fractions in equations?
3. How can you check if a solution is correct for an equation?
4. What are some methods to solve linear equations involving decimals?
5. How do you solve equations with multiple steps and fractions?

**Tip:** Always verify your solution by substituting it back into the original equation to ensure it satisfies both sides!

Discover how to solve the linear equation 5/3z + 1 = 3 - 2/3z. This problem involves algebraic techniques like eliminating fractions, combining like terms, and solving for the variable z. Ideal for students in Grades 6-8, it covers key steps to simplify and isolate variables.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation