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Solve for $u$ . $\newline$ $5 = |u - 2|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $u =$ _ or $u =$ _

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Solve absolute value equations

Full solution

Q. Solve for

u

.

\newline

5 = |u - 2|

\newline

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

\newline

u =

_____ or

u =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $5 = |u - 2|$ means that the expression inside the absolute value, $u - 2$ , is either $5$ or $-5$ , because the absolute value of a number is always non-negative.
Set up two equations: Set up two separate equations to solve for $u$ . Since $|u - 2|$ can be either $5$ or $-5$ , we have: $u - 2 = 5$ or $u - 2 = -5$
Solve first equation: Solve the first equation $u - 2 = 5$ . Add $2$ to both sides of the equation to isolate $u$ . $u - 2 + 2 = 5 + 2$ $u = 7$
Solve second equation: Solve the second equation $u - 2 = -5$ . Add $2$ to both sides of the equation to isolate $u$ . $u - 2 + 2 = -5 + 2$ $u = -3$

More problems from Solve absolute value equations

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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

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\newline

1

\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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