Question

Kuta Software - Infinite Algebra 2 Solving Absolute Value Equations Solve each equation. 1) 3x= 9 2) 1-3rl= x=3 and t-3 3 3

Answer 1

Given:

`|(n)/(3)|=2`

Let's solve the absolute value equation for n.

Take the following steps:

Step 1:

Remove the absolute value symbol, then add ± to the right hand side

`(n)/(3)=\pm2`

Step 2:

Here, we have two conditions. Solve the equation for both values

`\begin{gathered} \text{Condition 1:} \\ (n)/(3)=2 \\ \text{Multiply 3 to both sides:} \\ (n)/(3)*3=2*3 \\ \\ n=6 \end{gathered}`
`\begin{gathered} \text{Condition 2:} \\ (n)/(3)=-2 \\ Multiply\text{ both sides by 3} \\ (n)/(3)*3=-2*3 \\ \\ n=-6 \end{gathered}`

The solution of the absolute value equation includes both the negative and positive values.

Thus, we have:

n = 6, -6

ANSWER:

n = 6 and -6