To solve the equation:

\[
\frac{2}{5}(3x - 1) = \frac{1}{7}(5x + 4)
\]

we will follow these steps:

### Step 1: Eliminate the denominators
Multiply both sides of the equation by the least common denominator (LCD) of 5 and 7, which is 35, to eliminate the fractions.

\[
35 \times \left(\frac{2}{5}(3x - 1)\right) = 35 \times \left(\frac{1}{7}(5x + 4)\right)
\]

This simplifies to:

\[
7 \times (3x - 1) = 5 \times (5x + 4)
\]

### Step 2: Distribute
Now distribute both sides:

\[
7(3x - 1) = 5(5x + 4)
\]

This becomes:

\[
21x - 7 = 25x + 20
\]

### Step 3: Move terms with \(x\) to one side and constants to the other side
Subtract \(21x\) from both sides:

\[
-7 = 4x + 20
\]

Subtract 20 from both sides:

\[
-27 = 4x
\]

### Step 4: Solve for \(x\)
Now, divide both sides by 4:

\[
x = \frac{-27}{4}
\]

Thus, the solution is:

\[
x = -\frac{27}{4}
\]

---

Would you like a more detailed breakdown of any step or have any questions?

Here are 5 related questions:
1. How do you handle equations with fractions on both sides?
2. What is the least common denominator and how is it found?
3. How do you distribute multiplication across parentheses?
4. Can you explain how to move variables and constants to one side of an equation?
5. What are common strategies for solving linear equations?

**Tip:** Always check your solution by plugging it back into the original equation to verify correctness!

This guide provides a step-by-step solution to the linear equation 2/5(3x-1) = 1/7(5x+4), covering important algebraic concepts such as working with fractions, using the distributive property, and solving for variables. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation