Question

solve the linear equation for n. -20 = -n - 3(3n - 10)

Explanation:

Step1: Distribute the -3

First, we distribute the -3 into the parentheses \(3n - 10\). Using the distributive property \(a(b - c)=ab - ac\), we get:
\(-20=-n-3\times3n+(-3)\times(-10)\)
Simplifying the multiplication:
\(-20=-n - 9n+30\)

Step2: Combine like terms

Next, we combine the like terms \(-n\) and \(-9n\). Combining these gives:
\(-20=-10n + 30\)

Step3: Subtract 30 from both sides

To isolate the term with \(n\), we subtract 30 from both sides of the equation:
\(-20-30=-10n+30 - 30\)
Simplifying both sides:
\(-50=-10n\)

Step4: Divide both sides by -10

Finally, we divide both sides of the equation by -10 to solve for \(n\):
\(\frac{-50}{-10}=\frac{-10n}{-10}\)
Simplifying the division:
\(5 = n\)

Answer:

\(n = 5\)