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Solve for $f$ . $\newline$ $7 = |\text{-}f|$ $\newline$ 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

7 = |\text{-}f|

\newline

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

\newline

f =

_____ or

f =

_____

Understand the equation: Understand the equation $7 = |\text{-}f|$ . The absolute value of a number is always non-negative. Therefore, if $|\text{-}f| = 7$ , then $\text{-}f$ can be either $7$ or $-7$ because the absolute value of both $7$ and $-7$ is $7$ .
Solve for f when: Solve for f when $-f = 7$ . To find the value of $f$ , we need to get rid of the negative sign in front of $f$ . We do this by multiplying both sides of the equation by $-1$ . $-f = 7$ becomes $f = -7$ after multiplying by $-1$ .
Solve for $f$ when: Solve for $f$ when $-f = -7$ . Similarly, we multiply both sides of the equation by $-1$ . $-f = -7$ becomes $f = 7$ after multiplying by $-1$ .
Check the solutions: Check the solutions. $\newline$ We substitute $f = -7$ and $f = 7$ back into the original equation to verify that they are correct. $\newline$ For $f = -7$ : $7 = |–(-7)|$ simplifies to $7 = |7|$ , which is true. $\newline$ For $f = 7$ : $7 = |–(7)|$ simplifies to $7 = |-7|$ , which is also true. $\newline$ Both solutions satisfy the original equation.

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