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Solve for $z$ . $\newline$ $8 = |z| + 6$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $z =$ _ or $z =$ _

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Solve absolute value equations

Full solution

Q. Solve for

z

.

\newline

8 = |z| + 6

\newline

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

\newline

z =

_____ or

z =

_____

Isolate absolute value term: Isolate the absolute value term. $\newline$ Subtract $6$ from both sides of the equation to isolate $|z|$ . $\newline$ $8 - 6 = |z| + 6 - 6$ $\newline$ $2 = |z|$
Solve for $z$ : Solve for $z$ . $\newline$ Since $|z| = 2$ , $z$ can be either $2$ or $-2$ because the absolute value of both $2$ and $-2$ is $2$ . $\newline$ So, $z = 2$ or $z$ $0$ .

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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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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\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

5h+2.5t=200

\newline

2.5h+5t=200

Posted 8 months ago

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