Solve the equation.
`\frac{10w}{2}+7-8w=-8\left(6+w\right)`
To solve the equation, we will simplify both sides step-by-step.
Starting with the left side of the equation, we have:
\[\frac{10w}{2} + 7 - 8w\]
The first term, \(\frac{10w}{2}\), simplifies to \(5w\), so the equation becomes:
\[5w + 7 - 8w\]
Now, let's simplify the right side of the equation:
\[-8(6+w)\]
Expanding the expression in the parentheses, we have:
\[-8(6) - 8(w)\]
Which simplifies to:
\[-48 - 8w\]
Now the equation becomes:
\[5w + 7 - 8w = -48 - 8w\]
Combining like terms, we have:
\[-3w + 7 = -48 - 8w\]
Next, let's get rid of the parentheses on the right side by distributing the negative sign:
\[-3w + 7 = -48 + (-8w)\]
Simplifying further, we have:
\[-3w + 7 = -48 - 8w\]
Now, let's bring all the terms with \(w\) on one side and the constant terms on the other side. We can do this by adding \(8w\) to both sides:
\[-3w + 8w + 7 = -48 - 8w + 8w\]
This simplifies to:
\[5w + 7 = -48\]
Next, let's isolate \(w\) by subtracting 7 from both sides of the equation:
\[5w + 7 - 7 = -48 - 7\]
This gives us:
\[5w = -55\]
Finally, divide both sides of the equation by 5 to solve for \(w\):
\[\frac{5w}{5} = \frac{-55}{5}\]
Simplifying further, we find that:
\[w = -11\]
Therefore, the solution to the equation is \(w = -11\).