Question

solve the equation \\(\frac{10w + 8}{2}=5\\) for \\(w\\) using the distributive property of division, as in example 1. rewrite the expression on the left of the equals sign by dividing \\(10w + 8\\) by 2. \\(w + \square = 5\\) isolate the variable term by subtracting a constant from both sides of the equation. \\(w = \square\\) isolate the variable by dividing each side by the same number.

Explanation:

Step1: Rewrite the equation using division property

Given the equation \(\frac{10w + 8}{2}=5\), we can rewrite the left - hand side by dividing each term in the numerator by 2. Using the distributive property of division \(\frac{a + b}{c}=\frac{a}{c}+\frac{b}{c}\), we get \(5w+4 = 5\).

Step2: Isolate the variable term

To isolate the variable term \(5w\), we subtract 4 from both sides of the equation. According to the subtraction property of equality (if \(a=b\), then \(a - c=b - c\)), we have \(5w+4-4=5 - 4\), which simplifies to \(5w=1\).

Step3: Solve for \(w\)

To solve for \(w\), we divide both sides of the equation \(5w = 1\) by 5. Using the division property of equality (if \(a=b\), then \(\frac{a}{c}=\frac{b}{c}\) for \(c
eq0\)), we get \(w=\frac{1}{5}=0.2\).

Answer:

\(w = 0.2\) (or \(w=\frac{1}{5}\))