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 Asapppppppppppp

Answers

Answer:

(-15,0) and (0,-3)

Step-by-step explanation:

(-15,0) = x- intercept

(0,-3) = y-intercept

The function f(x) is defined below. What is the end behavior of f(x)?

Answers

Answer:

first choice

Step-by-step explanation:

Need help with math questions. :) Please help me answer them... I will give brainless

Answers

5.) red: slope is -2 and y-int is 1
Blue: slope is 1/2 and y-int is 3
Green: slope is -2/3 and y-int is -4

Answer:

7.)

a. y = -3x+3

b. y = 3x + 4

c. y = x + 3 (not sure about this one)

8.)

x = 63

y = 6

6.)

left an attachment (not sure about the growth triangle though)

5.)

Red Line - slope = -2

                 y-in = 1

Blue Line - slope = (1/2) or 0.5

                  y-in = 3

Green Line - slope = (-2/3) or 0.667

                    y-in = -4

Step-by-step explanation:

Sorry it took me so long

A full body treatment costs £125.00 Today there is a 10% discount, how much do you pay ?


Answers

Step-by-step explanation:

[tex] \frac{10}{100} \times 125 = 12.5 \\ 125 - 12.5 = 112.5[/tex]

112.5 £

112$ is how much you pay

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 8,300 miles. What proportion of these tires last between 40,000 and 45,000 miles

Answers

Answer:

P [ 40000 ≤ X ≤ 45000 ] =  0,02773    or  2,8 %

Step-by-step explanation:

P [ 40000 ≤ X ≤ 45000 ]  = ?

To find the probablity    P [ X ≤ 40000 ] =  ?

z(s)  = ( X - x ) / σ

z(s)= ( 40000 - 6000 )/ 8300

z(s) =  -20000/8300

z(s) ≈  - 2,41

Then

from z-table we find P [ X ≤ 40000] =  0,00820

Now again:

For  P [ X ≤ 45000 ]

z₂  = ( X - x ) / σ

z₂ =  ( 45000 - 6000 ) / 8300

z₂ = - 15000 / 8300

z₂ = - 1,8072

z₂ ≈ 1,81

From z - table

For  P [ X ≤ 45000 ] =   0,03593

Then:

P [ 40000 ≤ X ≤ 45000 ] = 0,03593 - 0,00820

P [ 40000 ≤ X ≤ 45000 ] =  0,02773    or  2,8 %

Find both the area and the perimeter of the semi circle

Answers

Answer/Step-by-step explanation:

Area of a semicircle = ½πr²

Perimeter of a semicircle = πr + d

7. d = 14 m

r = ½ of d = 7 m

Area = ½*π*7² = ½*π*49

✅Area = 76.97 m² (nearest hundredth)

Perimeter = π*7 + 14

✅Perimeter = 35.99 m (nearest hundredth)

8. d = 35 in.

r = ½ of d = 17.5 in.

Area = ½*π*17.5² = ½*π*306.25

✅Area = 481.06 in.² (nearest hundredth)

Perimeter = π*17.5 + 35

✅Perimeter = 89.98 in (nearest hundredth)

5.7 + 2(w + 1) = 2w + 9
- 8(4 + 9r) = 7(- 2 - 11r)

Answers

Answer:

Step-by-step explanation:

5.7 + 2(w+1)  = 2w + 9

5.7 + 2w + 2 = 2w + 9

7.7 = 9, which is impossible, so there is no solution.

:::::

-8(4+9r) = 7(-2-11r)

-32-72r = -14-77r

5r = 18

r = 3.6

Multiply.
(3x + 1)(x + 7)

Answers

Answer:

the answer is 3x^2 + 22x + 7

Step-by-step explanation:

Expand the polynomial using the FOIL method.

hoped this helped!

brainly, please?

Answer:

3x^2+22x+7

Step-by-step explanation:

y - 4= -8 (x - 1)
linear or nonlinear?

Answers

The answer would be it ~linear~

Hope this helps

Have a great day/night!
It’s linear because it going at a constant rate

Use the distributive property to rewrite the expression in factor form. 18h - 33

Answers

Answer:

you have to factor 3 out of 18h-33 so you get 3(6h-11)

reatest to Smallest which is correct?



1. 50 16 5 -64


2. 16 5 50 -64


3. 5 16 -64 50


4. -64 50 16 5

Answers

Answer:

1. 50 16 5 - 64

Step-by-step explanation:

have a nice day

50, 16, 5, -64
Minus numbers are always the smallest for example;
-10 is smaller than -70 because it is closer to positive numbers eg: 1,2,3 eg

Suppose that the local sales tax rate is 7% and you purchase a car for $14,100

a. How much tax is paid ?
B. What is the car's total cost ?

Answers

I don't understand you're language

Complete the ratio table with the numbers:
A) 18, 6, 44, 10
B) 20, 5, 45, 10
C) 24, 5, 48, 4
D) 28, 6, 44, 9

Answers

Answer:

C

24, 5, 48, 4 because blue is 6 times green

Step-by-step explanation:

Hope this helps

-8.5n = 17
pls help me

Answers

I believe the answer is n= -2

tangent 25 = x/15 rounded to nearest tenth

Answers

Answer:

Value of x = 7.0 units.

Step-by-step explanation:

Given the trigonometric equation

[tex]\tan \left(25^{\circ }\right)=\frac{x}{15}[/tex]

Switch sides

[tex]\frac{x}{15}=\tan \left(25^{\circ \:}\right)[/tex]

Multiply both sides by 15

[tex]\frac{15x}{15}=15\tan \left(25^{\circ \:}\right)[/tex]

Simplify

[tex]x=15\tan \left(25^{\circ \:}\right)[/tex]

∵ tan (25) = 0.46630

Thus,

x = 7.0     (rounded to nearest tenth)

Therefore, value of x = 7.0 units.

1. Set up a proportion and use it to solve for X.
16
12
X

Answers

x/12 = 12/16
x/12 = 3/4
4x = 36
x = 9

Check: 9/12 = 3/4 :)

plzzzzzzzzzzzzzzzzzzz helppppppppppppp meeeeeeeeee

Answers

Answer:

2m+14

Step-by-step explanation:

I hope its right

Answer:

2(m+14)

Step-by-step explanation:

m represents how much Ashton has.

-add 14 to how much Ashton has

(m+14) represents how much Riley has.

-multiply how much RIley has by 2

2(m+14) represents how much Peyton has.

Solve the system of linear equations by substitution. Check your solution.

Answers

Answer:

(x,y)= (- 2, - 1)

Step-by-step explanation:

Oscar wants to rent a boat. The rental company charges an initial fee of $12 plus $8 per hour to rent the boat.

a) Write a linear equation to describe the total cost of renting the boat.

b) What is the cost of renting the boat for 5 hours?

Answers

i need points pleaseeeeeeeeee

Answer:

a) y=8x+12

b) $52

Step-by-step explanation:

for a)

the linear cost of this equation is 8, since is asks this amount per hour. The constant is 12, a one time fee. to form the equation, you would use the formula y=mx+b, and substituted in with the given, you get y=8x+12.

for b)

in b, it asks for the cost of renting the boat when x=5, renting the boat for 5 hours. all you have to do is plug in 5 in place of the x in the equation:

y=8x+12

y=8(5)+12

y=40+12

y=52

Which of the following are factorable? Select the two correct answers. (2 points)
O Z2 – 21 – 15
22 +51 +2
22 – 51 +3
O2? +61 + 8

Answers

Answer:

First and last

Step-by-step explanation:

Find the what will multiple to the last number and add to the second number.

A teapot is 1/3 full of tea. When all of the tea is poured into an empty container, the container is 2/3 full. What fraction of the tea from a full cup is needed to fill 1 entire container?

Answers

1/3)t = (2/3)c, where "t" is for teapot and "c" is for the container.
Multiply both sides by (3/2) in order to get 1 on the right-hand side.
(3/2)(1/3)t = (3/2)(2/3)C
simplify the equation to get the answer which is:
(1/2) teacup = 1 full container.


Adam is making mini berry pies. For the filling, he mixes 1 pound each of raspberries,
blueberries, and blackberries. Then, he scoops 6 ounces of the filling into each mini pie tin. If
he wants to use up all of his filling, how many mini pies can he make?

Answers

Answer:

8 pies.

Step-by-step explanation:

Solve the system of equations
y equals 5 x plus 4
y equals 7 x plus 6

Answers

Answer:

x = -1 , y = -1

Step-by-step explanation:

We have system of equations and are asked to solve them.

We are looking for x and y, since both equations start with y, we can plug one to the other.

y = 5x + 4

y = 7x + 6

5x + 4 = 7x + 6

Now isolate x byitself to get x :

5x + 4 = 7x + 6

Subtract 4 from both sides :

5x = 7x + 2

Subtract 7x from both sides :

-2x = 2

Divide -2 by both sides :

x = -1

Now that we know what x is, we can substitute it into the equations seapraretly.

y = 5(-1) + 4

y = 7(-1) + 4

y = -5 + 4

y = -7 + 6

-5 + 4

-1

-7 + 6

-1

Therefore, both x and y equal -1

Step-by-step explanation:

5x4=20

7×6=42[tex]5 \times 4 = 20[/tex]

plz help me brainlest for the 1st answer

Answers

The answer is a medium Pizza of 12 inches radius.

The formula for finding the area of a square is pir^2(sorry but my phone won’t let me write pi in its symbol form). If we substitute 3 for pi, then that would the 3r^2. Then we would substitute the potential answer choices until we reach one that is closest to 400 in^2. For the small pizza, that would be 9*9*3, which is also 243 inches square. For the medium pizza, that would be 12*12*3, which is also 432 inches square. Finally, for the large pizza it is 15*15*3, which is 675. Therefore, the medium pizza has an area closest to inches square.

Dario puts 44 marbles in a box in which 14 are red, 12 are blue, and 18 are yellow. If Dario picks one marble at random, what is the probability that he selects a red marble or a yellow marble?

Answers

Answer:

not simplified: 18/44    

Simplified: 9/22

Step-by-step explanation:

Please Help
a in a complete sentence, describe the angle relationship in the diagram

Answers

The sum of angles is equal to 180 so they are called supplementary angles
The sum of angles is equal to 180 so they are called supplementary angles

What additional information must be known to prove the triangles similar by SAS?

Answers

Answer:

We must know what DF and JK are.

Step-by-step explanation:

SAS similarity is when two sides are proportional and the corresponding angles are congruent.

K and F are congruent (A)

KL and GF seem to have a proportion of 5/6 or 6/5 (S)

We need the other S to prove SAS.

Clare bought a photo for 19 cents and paid with a $1 bill. How much change should she receive? ASAP

Answers

81 cents. :))))))))((()

A light bulb consumes 3600 watt hours per day how long does it take to consume 15300 watt-hours

Answers

Answer:

4.25 days

Step-by-step explanation:

Divide 15300 by 3600 to get the amount of time it takes. It takes 4.25 days for the bulb to consume 15300 watt-hours.

Answer:

11700

Step-by-step explanation:

15300-3600=11700

nine times a number decreased by four

Answers

Answer: 9x - 4

Step-by-step explanation:

We know that a number must be decreased by four. Let's break it up a little.

Nine times some number. We don't know what nine will be multiplied by, so we will just write a placeholder number: x. This number will be multiplied by nine. So it will turn into 9x.

We must decrease (subtract) from this by four. Subtracting 9x by four can be written as 9x - 4.

The answer for this question is 9x-4
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