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Solve for $j$ . $\newline$ $5 = |\,-5j\,|$ $\newline$ 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

5 = |\,-5j\,|

\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 $5 = |-5j|$ means that the expression inside the absolute value, $-5j$ , can be 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 $j$ . Since $|-5j|$ can be either $5$ or $-5$ , we have two cases: Case $1$ : $-5j = 5$ Case $2$ : $-5j = -5$
Solve for $j$ in Case $1$ : Solve for $j$ in Case $1$ . $\newline$ Starting with $–5j = 5$ , we divide both sides by $-5$ to isolate $j$ . $\newline$ $j = \frac{5}{-5}$ $\newline$ $j = -1$
Solve for $j$ in Case $2$ : Solve for $j$ in Case $2$ . $\newline$ Starting with $–5j = -5$ , we divide both sides by $-5$ to isolate $j$ . $\newline$ $j = -5 / -5$ $\newline$ $j = 1$

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

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

Posted 8 months ago

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