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Solve for $f$ . $\newline$ $0 = |f + 9|$ $\newline$ 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

0 = |f + 9|

\newline

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

\newline

f =

_____ or

f =

_____

Identify Equation: Identify the equation to solve. $\newline$ The given equation is $0 = |f + 9|.$
Absolute Value Property: Understand the property of absolute value. $\newline$ The absolute value of a number is its distance from zero on the number line, which means it is always non-negative. If the absolute value of something is $0$ , then that something must be $0$ .
Set Expression Equal: Set the expression inside the absolute value equal to $0$ . Since $|f + 9| = 0$ , it follows that $f + 9 = 0$ .
Solve for f: Solve for f. $\newline$ Subtract $9$ from both sides of the equation to isolate $f$ . $\newline$ $f + 9 - 9 = 0 - 9$ $\newline$ $f = -9$
Check Other Solutions: Check for other possible solutions. $\newline$ Normally, if we have an equation like $|x| = a$ , we would also consider $x = -a$ . However, since $a$ is $0$ in this case, the only solution is $x = 0$ . Therefore, there is no second solution for $f$ .

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\$200

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