Why are inverse relationships between operations used to solve two step inequalities?

Answers

Answer 1

Answer:

The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation.

Reverse addition and subtraction (by subtracting and adding) outside parentheses. Reverse multiplication and division (by dividing and multiplying) outside parentheses. When multiplying or dividing by a negative number, flip the inequality sign. It does not matter if the number being divided is positive or negative

It's necessary to apply inverse operations on both sides of the equals signs so that you can solve for the variable and balance the equation.

Multi-step inequalities are solved using the same processes that work for solving equations with one exception. When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. (Much like when you divide by a negative number, the sign of the inequality must flip! Here's why: When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side!)

Answer 2

Answer:

Step-by-step explanation:

The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation.


Related Questions

HELP ASAP PLEASE! GIVING AWAY 30 POINTS AND BRAINLIEST!

Answers

Answer:

DB!

Step-by-step explanation:

Question a: 3+3+2+2 = 10 dinners

Question b: 15-30 and 30-45, because most people choose that range.

Hope I helped!

Answer:

a) 10 b) 2-3 dollars

Step-by-step explanation:

a) 3+3+2+2

b) (2+2+3+3)/2 equal 2.5 mean, range between them is 2 to 3

Select the algebraic expression for the word expression.

24 less than h

24 - h
24 - h

h - 24
h - 24

24 ÷ h
24 ÷ h

h

Answers

Step-by-step explanation:

The Answer Is 24 - h

As, 24 Is Less Than "h"

Select the correct answer.
What is the LCM of the numbers 3, 6, and 9?

A.
9
B.
18
C.
36
D.
54

Answers

Answer:

D

Because you have to find out what they could all equal up to

Answer:

d

Step-by-step explanation:

Jonas is buying fencing to surround his garden. If his garden has a perimeter of 36 feet, and fencing costs
$10.00 a yard, how much money will he need for the fencing?

Answers

Answer:

Step-by-step explanation:

$120

If f(x) = 9x-8, which of the following is the inverse of f(x)?
O A. f'(x) = *19
O B. f'(x) = x;
O c. f-'(x) = 48
X-9
O D. f-1(x) =
8

Answers

f(x) = 9x+8
y = 9x+8
x = 8y + 9
x-9 = 8y

x-9
----- = y
8

f-¹ =
x-9
------
8

A submarine was situated 832 feet below sea level. If it descends 289 feet, what is its new position?

Answers

It's new position is 1121 feet below sea level.

(In this problem u are descending into a negative value so it made sense for me to add for some reason).

Hope this helps and have a good day.

Also, as proof I included my calculator showing the logic behind it. Sorry for bad Camera quality.

-R3TR0 Z3R0

Simplify completely
[tex] \frac{2x - 24}{8} [/tex]
A)
[tex] \frac{x - 24}{4} [/tex]
[tex] \frac{x - 12}{4} [/tex]
C) 2x-3
D) x-3​

Answers

Hopes this helps:

Answer: A) x-24/4

Please answer these in a fraction form. Thank you have an AMAZING day!

1. 2/5 ÷ 3 1/10 = ?
2. 4 1/3 ÷ 4/7 = ?
3. 3 1/6 ÷ 9/10 = ?
4. 5/8 ÷ 2 7/12= ?​

Answers

Answer:

use Photomath app to answer your question.

The circumference of a circle measures 11.277 ft.
What is the measure of the diameter of this circle?

Answers

Answer:

3.590ft

Step-by-step explanation:

We know what the circumference of the circle is, and we need to find its diameter. Therefore, we need to find an equation that links the two together.

Well, what comes to mind is the fact that the circumeference, [tex]c[/tex], is equal to [tex]\pi[/tex] multiplied by the diameter, [tex]d[/tex]. We can express this like so:

[tex]c = \pi d[/tex].

In this scenario, we know what [tex]c[/tex] is, so we need to rearrange the formula to make [tex]d[/tex] the subject. Dividing both sides by [tex]\pi[/tex] will accomplish this, and gives us:

[tex]\frac{c}{\pi} = d[/tex].

So if we divide the circumference by [tex]\pi[/tex], we will find the diamater. Well,

[tex]\frac{11.277}{\pi} = 3.58958...[/tex]

and so to 3 decimal places we get the answer

[tex]d = 3.590\text{ft}[/tex].

the EXACT value of 2÷(0.01)2 is

Answers

The EXACT value of 2÷(0.01)2 is 100.

The question asks that we divide 2 by (0.01)2. Division is a basic mathematical operation. The expression in the question can be rewritten as [tex]\frac{2}{(0.01)2}[/tex].

The first step to take in order to determine the answer is to simplify the denominator. Bracket means to multiply. So, 0.01 would be multiplied by 2. 0.01 x 2 = 0.02. Now that the denominator has been simplified, divide the numerator by the denominator.

2 / 0.02 = 100

A similar question was answered here: https://brainly.com/question/22357901

The EXACT value of 2÷(0.01)2 is 100.

The question asks that we divide 2 by (0.01)2.

Division is a basic mathematical operation.

The expression in the question can be rewritten as : 2/ (0.01)2

now, we get,

The first step to take in order to determine the answer is to simplify the denominator.

Bracket means to multiply.

So, 0.01 would be multiplied by 2.

i.e. 0.01 x 2 = 0.02.

Now that the denominator has been simplified, divide the numerator by the denominator.

we get,

2 / 0.02 = 100

Learn more about the Division here:

brainly.com/question/22357901

#SPJ6

Please help I need this answer!

Answers

Answer: 16

Step-by-step explanation: Good luck! :D

Answer:

It’s 16

Good luck

I honestly lost most of my brain cells Bc of quarantine so I’m glad I figured this out

A garden table and a bench cost $903 combined. The garden table costs $53 more than the bench. What is the cost of the bench?

Answers

2x+53=903-53
2x=850 divide by two
x=425
bench - $425

I need help with this

look at picture

Complementary angles

Answers

Answer:

77

Step-by-step explanation:

48 + (x-35) = 90

x-35 = 90-48

x-35 = 42

x = 42+35

x = 77

What is the ratio of a:b, knowing that a-b/a+b = 3/5.

Answers

Answer:

4:1

Step-by-step explanation:

[tex]\frac{a-b}{a+b}[/tex] = [tex]\frac{3}{5}[/tex]

4-1 = 3

4+1 = 5

-3m + 5>26
How to answer this question

Answers

9514 1404 393

Answer:

  m < -7

Step-by-step explanation:

Maybe you want to find the value of m.

Subtract 5, then divide by -3.

  -3m +5 > 26 . . . given

  -3m > 21 . . . . . . subtract 5 from both sides

  m < -7 . . . . . . . . divide by -3. Dividing by a negative number reverses the inequality.

WILL GIVE BRAINLIEST GIVE CORRECT ANSWER

Answers

your answer is correct

Answer:

everything u chose is right

Step-by-step explanation:

50 = 20 + 4h

-20. -20

30/4= 4h/4

7.5 = h

So 50 = 20 + 4(7.5)

50 = 30 + 20

50 = 50

13 as prime or composite

Answers

Answer:

prime

gggghfsssddfdfv ut b dc t

Answer:

the number 13 is a prime number

Draw the proble. give me steps. Please​

Answers

Answer:

I cant draw 4 u sry

Answer:

A. c = 3.5h + 15

Step-by-step explanation:

I can't exactly draw the problem BUT I can still help.

C represents the cost altogether but we do not know how much the total cost would be.

So we're paying $15 as a fee, no more from that.

Next, there's another fee that costs $3.50 per hour but since we wouldn't know how long we would use the kayak, hours would represent h.

Now, c = 3.5h + 15.

(In other words, the cost to rent a kayak would be $3.5 PLUS the additonal 15 one time cost.)

MNOP is a trapezoid with bases MN and OP. If MN = 25 and OP = 23, what is the length of the midsegment of MNOP?

Answers

Answer:

24

Step-by-step explanation:

you can get the answer from the attachment

The midsegment of a trapezoid divides the trapezoid into equal parts.

The length of the midsegment of MNOP is 24

The lengths of the base are given as:

[tex]\mathbf{MN = 25}[/tex]

[tex]\mathbf{OP = 23}[/tex]

Let the midsegment be x.

So, we have:

[tex]\mathbf{x=\frac{1}{2}(MN + OP)}[/tex]

Substitute values for MN and OP

[tex]\mathbf{x=\frac{1}{2}(25 + 23)}[/tex]

[tex]\mathbf{x=\frac{1}{2}(48)}[/tex]

[tex]\mathbf{x=24}[/tex]

Hence, the midsegment of MNOP is 24

Read more about midsegments of trapezoids at:

https://brainly.com/question/7511906

can someone please help me with this math problem thank you.

Answers

The perimeter is 10.25 by adding all sides of the triangle. Using the formula for a triangle, (height times base)/2, the area is 5.
A). 10.25
B). 5 (I think)

X-4/x-3 is less than 2x-1/2

Answers

Answer:

yes

Step-by-step explanation:

yes

Do you mean x-(4/x)-3, or (x-4)/(x-3), or x-(4/(x-3)), or ((x-4)/x)-3, or something else?

Find the measure of each missing angle.​

Answers

9514 1404 393

Answer:

35°145°55°125°55°

Step-by-step explanation:

The right triangles are similar, so angle 1 is congruent to the given angle, and angles 3 and 5 are complements of that.

Angles 2 and 4 are the supplements of angles 1 and 5, respectively.

  ∠1 = 35°

  ∠2 = 180° -35° = 145°

  ∠3 = ∠5 = 90° -35° = 55°

  ∠4 = 180° -55° = 125°

Find the area of the circle. Use 3.14 for pi.






Question 1 options:


113.04 in2


56.52 in2


256.34 in2


1017.36 in2

Answers

Answer:

The answer is 254.34 in².

Step-by-step explanation:

Given that the diameter is 2 times the radius. So the radius will be 9 in. Next, you have to find the area of circle, A = π × r² :

A = π × r²

Let π = 3.14, r = 9,

A = 3.14 × 9²

A = 254.34 in²

Find the cos of angle T....

Answers

Answer:

C = 24/25

Step-by-step explanation:

Recall, CAH.

Thus:

Cos T = adjacent/hypotenuse

Reference angle = T

Adjacent = 24

Hypotenuse = 25

Therefore,

Cos T = 24/25

Please show work so i know how you got your answer..thank you and have a nice day<3

Answers

Answer:

V=whl=2·2.5·4=20

Step-by-step explanation:

Answer:

2880 feet³

Step-by-step explanation:

since the question is asking for cubic feet we know we're finding volume.

v=l·w·b

v=4·24·30

=2880

A prize was awarded to 24 women and 1010 men.
a. What fraction of the prize winners were women?
b. What fraction were men?

Answers

Answer:

[tex]W = \frac{12}{17}[/tex] -- Women

[tex]M = \frac{5}{17}[/tex] --- Men

Step-by-step explanation:

Given

[tex]Men = 10[/tex] --- not 1010

[tex]Women = 24[/tex]

Solving (a) Fraction of Women

This is calculated as:

[tex]W = \frac{Women}{Men + Women}[/tex]

Substitute values for Women and Men

[tex]W = \frac{24}{10+24}[/tex]

[tex]W = \frac{24}{34}[/tex]

Simplify fraction

[tex]W = \frac{12}{17}[/tex]

Solving (b) Fraction of Men

This is calculated as:

[tex]M = \frac{Men}{Men + Women}[/tex]

Substitute values for Women and Men

[tex]M = \frac{10}{10+24}[/tex]

[tex]M = \frac{10}{34}[/tex]

Simplify fraction

[tex]M = \frac{5}{17}[/tex]

Write an expression equivalent to the one below
-2m-8+4(3m-9)

Answers

Answer:

Step-by-step explanation:

Distribute the 4 into the parentheses.

[tex]-2m-8+12m-36[/tex]

Combine like terms

[tex]10m-44[/tex]

Answer:

10m - 44

Step-by-step explanation:

Apply the distributed property: 12m - 36Re-write expression: -2m - 8 + 12m - 36-2m + 12m = 10m8 + 36 = 44Put them together: 10m - 44

I hope this helps!

6(x - 1) = 6x - 1
what’s the answer ^^

Answers

Answer:

this is an identity which is true for all x values

Step-by-step explanation:

Perform the indicated multiplication.  We get:

6x - 1 = 6x -1

and see that this is an identity which is true for all x values.

helppp!! For the given solid figure, find the value of the variable.

Answers

9514 1404 393

Answer:

  10 cm

Step-by-step explanation:

The diameter of the cylinder is 6 cm, so the length designated 'c' is the hypotenuse of a right triangle with legs 6 cm and 8 cm.

The Pythagorean theorem tells you the hypotenuse is ...

  c^2 = (6 cm)^2 + (8 cm)^2 = 100 cm^2

  c = √(100 cm^2) = 10 cm

The value of c is 10 cm.

_____

You may recognize these numbers as double those of a 3-4-5 right triangle.

Please help me i am taking a test and i really need help

Answers

Answer:

31.4159in

Step-by-step explanation:

Answer:

31.4

Step-by-step explanation:

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