To solve the equation 

\[
\frac{5x + 2}{2} - \frac{5x - 2}{4} = 3,
\]

we'll first eliminate the fractions by finding a common denominator. The common denominator for 2 and 4 is 4. 

We can rewrite the equation as:

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

Now, combine the fractions:

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

Simplifying the numerator:

\[
2(5x + 2) - (5x - 2) = 10x + 4 - 5x + 2 = 5x + 6.
\]

So, we have:

\[
\frac{5x + 6}{4} = 3.
\]

Next, multiply both sides by 4 to eliminate the fraction:

\[
5x + 6 = 12.
\]

Now, isolate \(x\):

\[
5x = 12 - 6,
\]
\[
5x = 6,
\]
\[
x = \frac{6}{5} = 1.2.
\]

Thus, the solution is:

\[
\boxed{1.2}.
\]

If you have any questions or need further details, let me know! Here are some related questions you might consider:

1. How would you check if \(x = 1.2\) satisfies the original equation?
2. What would be the solution if the equation were \(\frac{5x + 2}{2} + \frac{5x - 2}{4} = 3\)?
3. Can you explain how to find the common denominator for fractions?
4. What happens if you change the right side of the equation to a different number?
5. How would you graph this equation to visualize the solution? 

**Tip:** Always check your solutions by substituting them back into the original equation.

Explore the solution to the equation 5x + 2/2 - 5x - 2/4 = 3 with a comprehensive step-by-step guide. This example illustrates key algebraic techniques, including eliminating fractions and isolating variables, 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