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Solve for $b$ . $\newline$ $0 = |b - 1|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $b =$ _ or $b =$ _

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Solve absolute value equations

Full solution

Q. Solve for

b

.

\newline

0 = |b - 1|

\newline

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

\newline

b =

_____ or

b =

_____

Set Equation Equal: We are given the equation $0 = |b - 1|$ . The absolute value of a number is $0$ if and only if the number inside the absolute value is $0$ . Therefore, we can set the expression inside the absolute value equal to $0$ . $\newline$ $b - 1 = 0$
Solve for b: Now, we solve for b by adding $1$ to both sides of the equation. $\newline$ $b - 1 + 1 = 0 + 1$ $\newline$ $b = 1$
Consider Negative Value: Since the absolute value of a number is also $0$ if the number inside is $0$ , we consider the possibility that the expression inside the absolute value could be the negative of $0$ , which is still $0$ . However, since $-0$ is the same as $0$ , we do not get a different solution for $b$ .

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

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\newline

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\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

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