Question

solve for n.
-9n - 10 = 5n + 8 + 10
n = \boxed{}

Explanation:

Step1: Simplify the right side

First, we simplify the right - hand side of the equation \(-9n - 10=5n + 8 + 10\). We add the constants on the right side: \(8 + 10=18\), so the equation becomes \(-9n-10 = 5n+18\).

Step2: Move the variable terms to one side

We want to get all the terms with \(n\) on one side. We can add \(9n\) to both sides of the equation to get rid of the \(-9n\) on the left. So, \(-9n-10 + 9n=5n + 18+9n\). Simplifying both sides, the left side becomes \(- 10\) and the right side becomes \(14n+18\). So now we have \(-10=14n + 18\).

Step3: Move the constant terms to the other side

Next, we subtract \(18\) from both sides to isolate the term with \(n\). \(-10-18=14n+18 - 18\). Calculating the left side: \(-10-18=-28\), and the right side becomes \(14n\). So we have \(-28 = 14n\).

Step4: Solve for n

To solve for \(n\), we divide both sides of the equation \(-28 = 14n\) by \(14\). \(\frac{-28}{14}=\frac{14n}{14}\). Simplifying, we get \(n=-2\).

Answer:

\(-2\)