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Solve for $r$ . $\newline$ $|3r| = 3$ $\newline$ 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

|3r| = 3

\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 $|3r| = 3$ means that the absolute value of $3$ times $r$ is equal to $3$ . The absolute value of a number is the distance of that number from $0$ on the number line, which is always non-negative. Therefore, $3r$ can either be $3$ or $-3$ .
Solve for positive $3r$ : Solve for $r$ when $3r$ is positive. $\newline$ If $3r = 3$ , then we divide both sides by $3$ to isolate $r$ . $\newline$ $r = \frac{3}{3}$ $\newline$ $r = 1$
Solve for negative $3r$ : Solve for $r$ when $3r$ is negative. $\newline$ If $3r = -3$ , then we divide both sides by $3$ to isolate $r$ . $\newline$ $r = -3 / 3$ $\newline$ $r = -1$

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

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\newline

c=f

c=g

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, 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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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

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