To solve the equation:

\[
-4w + \frac{4}{5} = -\frac{4}{5}w - \frac{7}{3}
\]

### Step 1: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD). The denominators are 5 and 3, and the LCD is 15. Multiply every term of the equation by 15:

\[
15 \left(-4w + \frac{4}{5}\right) = 15 \left(-\frac{4}{5}w - \frac{7}{3}\right)
\]

This gives:

\[
15(-4w) + 15\left(\frac{4}{5}\right) = 15\left(-\frac{4}{5}w\right) + 15\left(-\frac{7}{3}\right)
\]

Simplifying each term:

\[
-60w + 12 = -12w - 35
\]

### Step 2: Collect like terms
Move the \(w\)-terms to one side and constants to the other side:

\[
-60w + 12w = -35 - 12
\]

This simplifies to:

\[
-48w = -47
\]

### Step 3: Solve for \(w\)
Divide both sides by -48 to isolate \(w\):

\[
w = \frac{-47}{-48}
\]

\[
w = \frac{47}{48}
\]

So, the solution is:

\[
w = \frac{47}{48}
\]

Would you like further clarification or have any questions?

Here are 5 related questions you might find useful:
1. How do you solve similar equations with multiple variables?
2. What is the importance of finding the least common denominator (LCD)?
3. Can fractions be eliminated in equations with other methods?
4. How do you handle equations where terms have different powers of variables?
5. What strategies can simplify complex algebraic equations?

**Tip:** When solving equations with fractions, clearing the fractions early simplifies the process greatly.

Learn how to solve the linear equation -4w + 4/5 = -4/5w - 7/3 using a step-by-step approach. The solution covers key algebraic concepts such as eliminating fractions, finding the least common denominator, and simplifying linear equations. Ideal for students in Grades 8-10.

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