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Solve for all values of
a in simplest form.

15=|15-3a|
Answer:
a=

Solve for all values of $a$ in simplest form. $\newline$ $15=|15-3 a|$ $\newline$ Answer: $a=$

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Integer inequalities with absolute values

Full solution

Q. Solve for all values of

a

in simplest form.

\newline

15=|15-3 a|

\newline

Answer:

a=

Understand absolute value equation: Understand the absolute value equation. $\newline$ The absolute value of a number is the distance of that number from zero on the number line, regardless of direction. Therefore, $|15-3a|$ can be either $15-3a$ or $-(15-3a)$ because the absolute value of a number is always non-negative.
Set up two equations: Set up two separate equations to solve for $a$ . Since the absolute value expression can be positive or negative, we have two cases: Case $1$ : $15-3a = 15$ Case $2$ : $-\left(15-3a\right) = 15$
Solve for a in Case $1$ : Solve for a in Case $1$ . $\newline$ $15-3a = 15$ $\newline$ Subtract $15$ from both sides: $\newline$ $15 - 3a - 15 = 15 - 15$ $\newline$ $-3a = 0$ $\newline$ Divide both sides by $-3$ : $\newline$ $a = 0/-3$ $\newline$ $a = 0$
Solve for $a$ in Case $2$ : Solve for $a$ in Case $2$ . $\newline$ $- (15 - 3a) = 15$ $\newline$ Multiply both sides by $-1$ to remove the negative sign: $\newline$ $15 - 3a = -15$ $\newline$ Subtract $15$ from both sides: $\newline$ $15 - 3a - 15 = -15 - 15$ $\newline$ $-3a = -30$ $\newline$ Divide both sides by $-3$ : $\newline$ $a = -30 / -3$ $\newline$ $a$ $0$

More problems from Integer inequalities with absolute values

Question

g

can be thought of as a scaled version of

f(x)=|x|

\newline

What is the equation for

g(x)

\newline

1

\newline

g(x)=-\frac{4}{3}|x|

\newline

g(x)=\frac{4}{3}|x|

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g(x)=-\frac{3}{4}|x|

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g(x)=\frac{3}{4}|x|

Posted 2 months ago

Question

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{5}{3}

\newline

What is the equation of the new graph?

\newline

1

\newline

y=-\frac{5}{3}|x|

\newline

y=\frac{3}{5}|x|

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y=-|x-5|+3

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y=|x-3|+5

Posted 4 months ago

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

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80

\mathrm{t}

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

h

, and the number of

\mathrm{t}

t

, that Aiden could purchase with this money?

\newline

1

\newline

40 h+80 t=400

\newline

80 h+40 t=200

\newline

5 h+2.5 t=200

\newline

2.5 h+5 t=200

Posted 4 months ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right.

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One of the intersection points is

(-2,2)

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Find the other intersection point. Your answer must be exact.

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Question

\mathbf{2 2}

dollars. Colleen has

x

dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?

\newline

1

\newline

x-22

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x+22

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22 x

\newline

22 x+22

Posted 4 months ago

Question

Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of

30

meters and a depth of

15

meters. He wants to increase the radius to

40

meters and the depth to

20

meters. How much more water will the pond hold, in thousands of cubic meters?

\newline

(Round to the nearest thousand cubic meters.)

Posted 25 days ago

Question

Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are

36

inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?

\newline

1

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32

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42

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55

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Posted 18 days ago

Question

Ari thinks the perfect milkshake has

5

scoops of ice cream for every

3

spoonfuls of caramel. Freeze Zone makes batches of milkshakes with

10

scoops of ice cream and

7

spoonfuls of caramel.

\newline

What will Ari think about the amount of caramel in Freeze Zone's milkshakes?

\newline

1

\newline

(A) Freeze Zone's milkshakes have too much caramel.

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(B) Freeze Zone's milkshakes have too little caramel.

\newline

(C) Freeze Zone's milkshakes are just right.

Posted 2 months ago

Question

Nayeli lights a

4 \mathrm{~m}^{2}

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10 \mathrm{~m}^{2}

30

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Whose space is lit brighter?

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1

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(A) Nayeli's area

\newline

(B) Citlali's area

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(C) The spaces are equally bright.

Posted 4 months ago

Question

Lashawn makes scrambled eggs with

3

spoonfuls of salsa for every

2

eggs. Gilberta adds

7

spoonfuls of salsa for every

5

\newline

Whose scrambled eggs have a stronger salsa taste?

\newline

1

\newline

(A) Lashawn's eggs

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(B) Gilberta's eggs

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(C) The dishes of scrambled eggs have equal salsa tastes.

Posted 2 months ago