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Solve for $j$ . $\newline$ $|j - 4| = 1$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $j =$ _ or $j =$ _

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Solve absolute value equations

Full solution

Q. Solve for

j

.

\newline

|j - 4| = 1

\newline

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

\newline

j =

_____ or

j =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $|j - 4| = 1$ means that the expression inside the absolute value, $j - 4$ , is either $1$ or $-1$ , because the absolute value of a number is the distance from zero, and it is always non-negative.
Set up two equations: Set up two separate equations to solve for $j$ . Since $|j - 4|$ can be either $1$ or $-1$ , we write two equations: $j - 4 = 1$ and $j - 4 = -1$
Solve first equation for j: Solve the first equation for j. $\newline$ $j - 4 = 1$ $\newline$ Add $4$ to both sides to isolate j. $\newline$ $j = 1 + 4$ $\newline$ $j = 5$
Solve second equation for j: Solve the second equation for j. $\newline$ $j - 4 = -1$ $\newline$ Add $4$ to both sides to isolate $j$ . $\newline$ $j = -1 + 4$ $\newline$ $j = 3$

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

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\newline

1

\newline

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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

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t-shirts. Which of the following best models the relationship between the number of hats,

h

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\newline

1

\newline

40h+80t=400

\newline

80h+40t=200

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2.5h+5t=200

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