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Solve for $f$ . $\newline$ $|f + 3| = 2$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $f =$ _ or $f =$ _

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Solve absolute value equations

Full solution

Q. Solve for

f

.

\newline

|f + 3| = 2

\newline

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

\newline

f =

_____ or

f =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $|f + 3| = 2$ means that the expression inside the absolute value, $f + 3$ , can either be $2$ or $-2$ , because the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Set up two equations: Set up two separate equations to solve for $f$ . Since $|f + 3|$ can be either $2$ or $-2$ , we have two cases: Case $1$ : $f + 3 = 2$ Case $2$ : $f + 3 = -2$
Solve first case: Solve the first case. $\newline$ For the first case, subtract $3$ from both sides to isolate $f$ : $\newline$ $f + 3 = 2$ $\newline$ $f = 2 - 3$ $\newline$ $f = -1$
Solve second case: Solve the second case. $\newline$ For the second case, subtract $3$ from both sides to isolate $f$ : $\newline$ $f + 3 = -2$ $\newline$ $f = -2 - 3$ $\newline$ $f = -5$

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3 n^{2}=27

\newline

What are the solutions to the given equation?

\newline

1

\newline

n=\sqrt{3}

\newline

n=3

\newline

n=-\sqrt{3}

n=\sqrt{3}

\newline

n=-3

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\newline

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Question

\$200

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\newline

1

\newline

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\newline

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