To solve the equation \(8\left(\frac{2x}{7} + 1\right) = \left(\frac{25x}{7} + 3\right)\), we can follow these steps:

1. **Distribute the 8** on the left side:
   \[
   8 \cdot \frac{2x}{7} + 8 \cdot 1 = \frac{16x}{7} + 8
   \]

2. **Rewrite the equation**:
   \[
   \frac{16x}{7} + 8 = \frac{25x}{7} + 3
   \]

3. **Eliminate the fractions** by multiplying the entire equation by 7:
   \[
   7\left(\frac{16x}{7} + 8\right) = 7\left(\frac{25x}{7} + 3\right)
   \]
   This simplifies to:
   \[
   16x + 56 = 25x + 21
   \]

4. **Rearrange the equation** to isolate \(x\):
   \[
   56 - 21 = 25x - 16x
   \]
   \[
   35 = 9x
   \]

5. **Solve for \(x\)**:
   \[
   x = \frac{35}{9}
   \]

Thus, the solution to the equation is:
\[
x = \frac{35}{9}
\]

### Questions for Further Understanding:
1. What would happen if we had different coefficients on \(x\)?
2. How can you verify the solution by substituting \(x\) back into the original equation?
3. What is the graphical representation of this equation?
4. Can you simplify or approximate \(\frac{35}{9}\)?
5. What are similar equations where you can apply this method?

### Tip:
When solving equations, always check your work by substituting your solution back into the original equation to ensure both sides are equal.

Discover how to solve the linear equation 8(2x/7 + 1) = (25x/7 + 3) with a step-by-step explanation. This guide covers key algebra concepts such as distribution and solving for x. Ideal 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