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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|

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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 8 months ago

Question

y=|x|

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\frac{5}{3}

\newline

What is the equation of the new graph?

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1

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

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

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y=-|x-5|+3

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Posted 10 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}

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h

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\mathrm{t}

t

, that Aiden could purchase with this money?

\newline

1

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40 h+80 t=400

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80 h+40 t=200

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5 h+2.5 t=200

\newline

2.5 h+5 t=200

Posted 10 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

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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

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1

\newline

x-22

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x+22

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22 x

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22 x+22

Posted 10 months ago

Question

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

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meters and a depth of

15

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(Round to the nearest thousand cubic meters.)

Posted 4 months 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

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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?

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1

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32

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42

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55

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Posted 7 months 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 8 months ago

Question

Nayeli lights a

4 \mathrm{~m}^{2}

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Whose space is lit brighter?

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1

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(A) Nayeli's area

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(B) Citlali's area

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(C) The spaces are equally bright.

Posted 5 months ago

Question

Lashawn makes scrambled eggs with

3

spoonfuls of salsa for every

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eggs. Gilberta adds

7

spoonfuls of salsa for every

5

\newline

Whose scrambled eggs have a stronger salsa taste?

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1

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(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 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant