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Solve for $r$ . $\newline$ $|r - 8| = 2$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $r =$ _ or $r =$ _

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Solve absolute value equations

Full solution

Q. Solve for

r

.

\newline

|r - 8| = 2

\newline

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

\newline

r =

_____ or

r =

_____

Understand absolute value equation: Understand the absolute value equation $|r - 8| = 2$ . $\newline$ The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|r - 8| = 2$ means that the expression $(r - 8)$ is $2$ units away from zero. This can happen in two ways: either $(r - 8) = 2$ or $(r - 8) = -2$ .
Set up two equations: Set up two separate equations to solve for $r$ . Since $|r - 8|$ can be either $2$ or $-2$ , we write two equations: $1$ ) $r - 8 = 2$ $2$ ) $r - 8 = -2$
Solve first equation: Solve the first equation $r - 8 = 2$ . Add $8$ to both sides of the equation to isolate $r$ . $r - 8 + 8 = 2 + 8$ $r = 10$
Solve second equation: Solve the second equation $r - 8 = -2$ . Add $8$ to both sides of the equation to isolate $r$ . $r - 8 + 8 = -2 + 8$ $r = 6$

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\newline

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\$200

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