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Solve for $c$ . $\newline$ $4 = |2c|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $c =$ _ or $c =$ _

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Solve absolute value equations

Full solution

Q. Solve for

c

.

\newline

4 = |2c|

\newline

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

\newline

c =

_____ or

c =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $4 = |2c|$ means that the absolute value of $2c$ is equal to $4$ . The absolute value of a number is always non-negative, so $2c$ can either be $4$ or $-4$ .
Set up two equations: Set up two separate equations to solve for $c$ . Since $|2c|$ can be $4$ or $-4$ , we have two cases: Case $1$ : $2c = 4$ Case $2$ : $2c = -4$
Solve first case: Solve the first case. $\newline$ For the first case, $2c = 4$ , divide both sides by $2$ to solve for $c$ . $\newline$ $c = \frac{4}{2}$ $\newline$ $c = 2$
Solve second case: Solve the second case. $\newline$ For the second case, $2c = -4$ , divide both sides by $2$ to solve for $c$ . $\newline$ $c = -4 / 2$ $\newline$ $c = -2$

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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, which of the following is the value of

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\newline

1

\newline

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\newline

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\newline

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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

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\newline

2.5h+5t=200

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