Questions: Solve the equation for the given variable. If your answer is a fraction, write it in fractional form. Do NOT convert the answer to a decimal. (w+3)/4-5=(w-3)/5 Answer: w=

Solution Steps

To solve the equation \(\frac{w+3}{4} - 5 = \frac{w-3}{5}\), we need to isolate the variable \(w\). Here are the high-level steps:

1. Eliminate the fractions by finding a common denominator.
2. Simplify the equation to isolate \(w\).
3. Solve for \(w\).

Starting with the equation:

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

we can eliminate the fractions by multiplying through by the least common multiple of the denominators, which is 20:

\[ 20 \left(\frac{w+3}{4}\right) - 20(5) = 20 \left(\frac{w-3}{5}\right) \]

This simplifies to:

\[ 5(w + 3) - 100 = 4(w - 3) \]

Distributing the terms gives us:

\[ 5w + 15 - 100 = 4w - 12 \]

Combining like terms results in:

\[ 5w - 85 = 4w - 12 \]

To isolate \(w\), we subtract \(4w\) from both sides:

\[ 5w - 4w - 85 = -12 \]

This simplifies to:

\[ w - 85 = -12 \]

Next, we add 85 to both sides:

\[ w = 73 \]

Final Answer