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Solve for $m$ . $\newline$ $1 = |m - 5|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $m =$ _ or $m =$ _

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Solve absolute value equations

Full solution

Q. Solve for

m

.

\newline

1 = |m - 5|

\newline

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

\newline

m =

_____ or

m =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $1 = |m − 5|$ means that the expression inside the absolute value, $m − 5$ , is either $1$ or $-1$ , because the absolute value of a number is the distance from zero, which is always positive or zero.
Set up two equations: Set up two separate equations to solve for $m$ . $\newline$ Since $|m - 5|$ can be either $1$ or $-1$ , we have two cases: $\newline$ Case $1$ : $m - 5 = 1$ $\newline$ Case $2$ : $m - 5 = -1$
Solve for $m$ in Case $1$ : Solve for $m$ in Case $1$ . $\newline$ Starting with $m - 5 = 1$ , add $5$ to both sides to isolate $m$ . $\newline$ $m - 5 + 5 = 1 + 5$ $\newline$ $m = 6$
Solve for $m$ in Case $2$ : Solve for $m$ in Case $2$ . $\newline$ Starting with $m - 5 = -1$ , add $5$ to both sides to isolate $m$ . $\newline$ $m - 5 + 5 = -1 + 5$ $\newline$ $m = 4$

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

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\newline

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\newline

3+\sqrt{11}

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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 2 months ago