https://file.aiquickdraw.com/mathbot/file/17253868316349fgilsqj.jpg

Let's solve the equation provided in the image:

\[
6 = \frac{1}{5}w + \frac{7}{5}w - 4
\]

### Step 1: Combine like terms
First, combine the terms involving \( w \) on the right-hand side:

\[
\frac{1}{5}w + \frac{7}{5}w = \frac{1+7}{5}w = \frac{8}{5}w
\]

So the equation now becomes:

\[
6 = \frac{8}{5}w - 4
\]

### Step 2: Isolate the variable \( w \)
Next, we'll add 4 to both sides of the equation to isolate the term with \( w \):

\[
6 + 4 = \frac{8}{5}w
\]

\[
10 = \frac{8}{5}w
\]

### Step 3: Solve for \( w \)
To solve for \( w \), multiply both sides by the reciprocal of \(\frac{8}{5}\), which is \(\frac{5}{8}\):

\[
w = 10 \times \frac{5}{8}
\]

\[
w = \frac{50}{8} = 6.25
\]

So, the solution is:

\[
w = 6.25
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would you solve the equation if the right-hand side was \( \frac{1}{5}w + \frac{7}{5}w + 4 \)?
2. What happens if you multiply the entire original equation by 5? How does that simplify the solution process?
3. How can you verify that \( w = 6.25 \) is indeed the solution to the equation?
4. What are the steps to solve an equation if the terms with \( w \) were on opposite sides of the equation?
5. How does solving this equation change if you use decimal equivalents instead of fractions?

**Tip:** Always double-check your work by substituting your solution back into the original equation to see if it satisfies the equation.

Learn how to solve the linear equation 6 = (1/5)w + (7/5)w - 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including combining like terms and solving for the variable. Suitable for students in Grades 8-10.

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