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Solve for $n$ . $\newline$ $|n + 5| = 2$ $\newline$ 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 + 5| = 2

\newline

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

\newline

n =

_____ or

n =

_____

Given Equation: We are given the absolute value equation $|n + 5| = 2$ . The absolute value of a number is the distance of that number from $0$ on the number line, which means it is always non-negative. Therefore, $n + 5$ can either be $2$ or $-2$ . We will solve for $n$ using both possibilities.
Case $1$ : Positive: First, let's consider the case where $n + 5$ is positive. We set $n + 5$ equal to $2$ and solve for $n$ . $\newline$ $n + 5 = 2$ $\newline$ Subtract $5$ from both sides to isolate $n$ . $\newline$ $n = 2 - 5$ $\newline$ $n = -3$
Case $2$ : Negative: Now, let's consider the case where $n + 5$ is negative. We set $n + 5$ equal to $-2$ and solve for $n$ . $\newline$ $n + 5 = -2$ $\newline$ Subtract $5$ from both sides to isolate $n$ . $\newline$ $n = -2 - 5$ $\newline$ $n = -7$

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