Question

#3
10n - 1 = 99

what is the first step to solve equation #3?
1 point
add -10 to both sides
add 1 to both sides
divide both sides by 10
subtract 1 from both sides

what is the second step to solve equation #3?
1 point
add 1 to both sides
subtract 1 from both sides
divide both sides by 10
add 10 to both sides

what is the solution to equation #3?
1 point
n = 10
n = 8
n = 15
none of the above

Explanation:

First Step Question

To solve the linear equation \(10n - 1 = 99\), we follow the order of operations in reverse (undoing operations). The first operation to undo is the subtraction of 1. To undo subtraction, we use addition. So we add 1 to both sides to isolate the term with \(n\) (i.e., \(10n\)).

After the first step (adding 1 to both sides, resulting in \(10n = 100\)), the next operation to undo is the multiplication of \(n\) by 10. To undo multiplication, we use division. So we divide both sides by 10 to solve for \(n\).

Step 1: Add 1 to both sides

To isolate the term with \(n\), we add 1 to both sides of the equation \(10n - 1 = 99\).
\[

$$\begin{align*} 10n - 1 + 1 &= 99 + 1\\ 10n &= 100 \end{align*}$$

\]

Step 2: Divide both sides by 10

To solve for \(n\), we divide both sides of the equation \(10n = 100\) by 10.
\[

$$\begin{align*} \frac{10n}{10} &= \frac{100}{10}\\ n &= 10 \end{align*}$$

\]

Answer:

B. Add 1 to both sides

Second Step Question