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Solve for $k$ . $\newline$ $6 = |\text{-}3k|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $k =$ _ or $k =$ _

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Solve absolute value equations

Full solution

Q. Solve for

k

.

\newline

6 = |\text{-}3k|

\newline

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

\newline

k =

_____ or

k =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $6 = |\text{-}3k|$ means that the absolute value of $\text{-}3k$ is equal to $6$ . The absolute value of a number is always non-negative, so we need to find the value of $k$ that makes $\text{-}3k$ equal to $6$ or $\text{-}6$ .
Set up two equations: Set up two separate equations to solve for $k$ . Since the absolute value of $–3k$ is $6$ , we can write two equations: one for the positive case and one for the negative case. Equation $1$ : $–3k = 6$ Equation $2$ : $–3k = -6$
Solve first equation for k: Solve the first equation for $k$ . Starting with Equation $1$ : $–3k = 6$ , we divide both sides by $-3$ to isolate $k$ . $k = \frac{6}{-3}$ $k = -2$
Solve second equation for k: Solve the second equation for k. $\newline$ Now, we solve Equation $2$ : $-3k = -6$ . Again, we divide both sides by $-3$ to isolate $k$ . $\newline$ $k = -6 / -3$ $\newline$ $k = 2$

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

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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

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\newline

1

\newline

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