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Solve for $z$ . $\newline$ $|z + 3| = 1$ $\newline$ 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

|z + 3| = 1

\newline

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

\newline

z =

_____ or

z =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $|z + 3| = 1$ means that the quantity $z + 3$ is $1$ unit away from $0$ on the number line. This can happen in two ways: either $z + 3$ is $1$ or $z + 3$ is $-1$ .
Solve for positive z: Solve for z when $z + 3$ is positive. $\newline$ If $z + 3 = 1$ , then we subtract $3$ from both sides to find the value of z. $\newline$ $z + 3 - 3 = 1 - 3$ $\newline$ $z = -2$
Solve for negative $z$ : Solve for $z$ when $z + 3$ is negative. $\newline$ If $z + 3 = -1$ , then we subtract $3$ from both sides to find the value of $z$ . $\newline$ $z + 3 - 3 = -1 - 3$ $\newline$ $z = -4$

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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