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Solve for $n$ . $\newline$ $|n + 4| = 1$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $n =$ _ or $n =$ _

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Solve absolute value equations

Full solution

Q. Solve for

n

.

\newline

|n + 4| = 1

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

n =

_____ or

n =

_____

Define Absolute Value: We are given the equation $|n + 4| = 1$ . To find the value of $n$ , we need to consider the definition of absolute value, which states that if $|x| = a$ , then $x = a$ or $x = -a$ . Therefore, we have two cases to consider for $n + 4$ : it can either be $1$ or $-1$ .
Case $1$ : $n + 4 = 1$ : Let's first consider the case where $n + 4 = 1$ . To solve for $n$ , we subtract $4$ from both sides of the equation. $\newline$ $n + 4 - 4 = 1 - 4$ $\newline$ $n = -3$
Case $2$ : $n + 4 = -1$ : Now let's consider the second case where $n + 4 = -1$ . Again, we solve for $n$ by subtracting $4$ from both sides of the equation. $\newline$ $n + 4 - 4 = -1 - 4$ $\newline$ $n = -5$

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