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Solve for $y$ . $\newline$ $0 = |-4y|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $y =$ _ or $y =$ _

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Solve absolute value equations

Full solution

Q. Solve for

y

.

\newline

0 = |-4y|

\newline

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

\newline

y =

_____ or

y =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation given is $0 = |–4y|$ . The absolute value of any number is always non-negative. Therefore, the only way for the absolute value of something to equal zero is for the inside of the absolute value to be zero.
Set inside equal to zero: Set the inside of the absolute value equal to zero. $\newline$ Since $|-4y| = 0$ , we can say that $-4y$ must equal $0$ because that's the only value whose absolute value is $0$ .
Solve for y: Solve for y. $\newline$ To find $y$ , we divide both sides of the equation $–4y = 0$ by $–4$ . $\newline$ $y = 0 / –4$ $\newline$ $y = 0$
Check for second solution: Check for a second solution. $\newline$ Normally, with absolute value equations, we would check for a second solution by setting the inside of the absolute value equal to the negative of the other side. However, since the other side of the equation is $0$ , the negative of $0$ is still $0$ . Therefore, there is no second solution in this case.

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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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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