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Solve for $r$ . $\newline$ $|-2r| = 6$ $\newline$ 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

|-2r| = 6

\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. $\newline$ The equation $|-2r| = 6$ means that the absolute value of $-2r$ is equal to $6$ . The absolute value of a number is its distance from zero on the number line, which means it is always non-negative. Therefore, $-2r$ can either be $6$ or $-6$ .
Set up two equations: Set up two separate equations to solve for $r$ . Since the absolute value of $–2r$ is $6$ , we can write two equations: one for the positive case and one for the negative case. $1$ ) $–2r = 6$ $2$ ) $–2r = -6$
Solve first equation: Solve the first equation $-2r = 6$ . $\newline$ Divide both sides by $-2$ to isolate $r$ . $\newline$ $r = \frac{6}{-2}$ $\newline$ $r = -3$
Solve second equation: Solve the second equation $–2r = -6$ . $\newline$ Divide both sides by $-2$ to isolate $r$ . $\newline$ $r = \frac{-6}{-2}$ $\newline$ $r = 3$

More problems from Solve absolute value equations

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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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\newline

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\newline

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\newline

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Question

\$200

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\newline

1

\newline

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