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Solve for $r$ . $\newline$ $5 = |5r|$ $\newline$ 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

5 = |5r|

\newline

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

\newline

r =

_____ or

r =

_____

Find Absolute Value: $5 = |5r|$ $\newline$ Find the value of $|5r|$ . $\newline$ Since the absolute value of a number is always non-negative and $5$ is positive, $|5r|$ can be equal to $5$ or $-5$ .
Find $r$ for $|5r| = 5$ : $|5r| = 5$ $\newline$ Find the values of $r$ . $\newline$ If $|x| = a$ , then $x = a$ or $x = -a$ . $\newline$ So, $5r = 5$ or $5r = -5$ .
Find $r$ for $|5r| = -5$ : Solve for $r$ when $5r = 5$ . $\newline$ Divide both sides by $5$ . $\newline$ $r = \frac{5}{5}$ $\newline$ $r = 1$
Find $r$ for $|5r| = -5$ : Solve for $r$ when $5r = 5$ . $\newline$ Divide both sides by $5$ . $\newline$ $r = \frac{5}{5}$ $\newline$ $r = 1$ Solve for $r$ when $5r = -5$ . $\newline$ Divide both sides by $5$ . $\newline$ $|5r| = -5$ $0$ $\newline$ $|5r| = -5$ $1$

More problems from Solve absolute value equations

Question

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

n=3

Posted 10 months ago

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6=3 x

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Question

\frac{1}{2} c^{2}+3 c=1

\newline

c=f

c=g

be the solutions to the given equation. If

f>g

, which of the following is the value of

f

\newline

1

\newline

-3+\sqrt{2}

\newline

-3+\sqrt{11}

\newline

3+\sqrt{2}

\newline

3+\sqrt{11}

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\ln (x-3)=1+\ln 2

\newline

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\newline

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\newline

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that solves the equation

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\newline

x=

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\newline

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Question

\$200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

hats. If Aiden purchases only t-shirts, he will get

80

t-shirts. Which of the following best models the relationship between the number of hats,

h

, and the number of t-shirts,

t

, that Aiden could purchase with this money?

\newline

1

\newline

40h+80t=400

\newline

80h+40t=200

\newline

5h+2.5t=200

\newline

2.5h+5t=200

Posted 8 months ago

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