Let's solve the equation \( \frac{4}{5}x + 6 = 4 \).

### Step 1: Isolate the variable term
Start by subtracting 6 from both sides of the equation:

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

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

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides by the reciprocal of \( \frac{4}{5} \), which is \( \frac{5}{4} \):

\[
x = -2 \times \frac{5}{4}
\]

\[
x = \frac{-10}{4}
\]

### Step 3: Simplify the result
Simplify the fraction:

\[
x = \frac{-5}{2}
\]

So, the solution is \( x = \frac{-5}{2} \) or \( -2.5 \).

Would you like more details on any step, or have any questions?

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Here are 5 related questions you might find helpful:

1. How do you solve equations with fractions in more complex cases?
2. What are other ways to solve linear equations with fractions?
3. Can we solve the same equation using a graphing method?
4. How do you check if your solution to a linear equation is correct?
5. How can equations be simplified before solving?

**Tip**: Always perform the same operation on both sides of an equation to maintain balance!

This page explains how to solve the linear equation 4/5x + 6 = 4 using algebraic methods. Learn to isolate the variable, eliminate fractions, and simplify the result, making it ideal for students in Grades 6-8.

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