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Solve for $u$ . $\newline$ $4 = |u - 4|$ $\newline$ 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

4 = |u - 4|

\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 $4 = |u − 4|$ means that the expression inside the absolute value, $u − 4$ , can either be $4$ or $-4$ , because the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Set up two equations: Set up two separate equations to solve for $u$ . Since $|u - 4|$ can be either $4$ or $-4$ , we have two cases: Case $1$ : $u - 4 = 4$ Case $2$ : $u - 4 = -4$
Solve first case: Solve the first case. $\newline$ For the first case, $u - 4 = 4$ , add $4$ to both sides to isolate $u$ : $\newline$ $u - 4 + 4 = 4 + 4$ $\newline$ $u = 8$
Solve second case: Solve the second case. $\newline$ For the second case, $u - 4 = -4$ , add $4$ to both sides to isolate $u$ : $\newline$ $u - 4 + 4 = -4 + 4$ $\newline$ $u = 0$

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\newline

What are the solutions to the given equation?

\newline

1

\newline

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\newline

n=3

\newline

n=-\sqrt{3}

n=\sqrt{3}

\newline

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\newline

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Question

\$200

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\newline

1

\newline

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