How do you solve and graph inequalities in algebra?

Answers

Answer 1

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality.

What are the steps to graphing an inequality?

The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

Here show an example for better understanding:

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.

To know more about inequality refer to:

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Related Questions

Plz help i don't wnat links i want you to show the answer on here i trust you will.
A=__in^2 i will give the brainlist 20 points btw

Answers

Answer:

a to L is 12 inches and a to n is 32 in                                                                          Step-by-step explanation:

Please help me with this

Answers

Answer:

x = 5

Step-by-step explanation:

Given

- 3x - 2 = - 17 ( add 2 to both sides )

- 3x = - 15 ( divide both sides by - 3 )

x = 5

Solve -4x + 6(x + 2) = 20.

Answers

Answer:

4

Step-by-step explanation:

-4x +6x +12 = 20

2x + 12 = 20

2x = 8

x = 4

Answer:

X=4

Step-by-step explanation:

-4x+6x+12=29

2x=8

x=4

Good luck .

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.(Quadratic Word Problems (Profit/Gravity)
y=-16x^2+121x+83

Answers

Answer:

The rocket will hit the ground after about 8.20 seconds.

Step-by-step explanation:

The height of the rocket y, in feet, x seconds after launch is modeled by the equation:

[tex]y=-16x^2+121x+83[/tex]

We want to find the time at which the rocket will hit the ground.

If it hits the ground, the height of the rocket y will be 0. Thus:

[tex]0=-16x^2+121x+83[/tex]

We can solve for x. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = -16, b = 121, and c = 83. Substitute:

[tex]\displaystyle x=\frac{-(121)\pm\sqrt{(121)^2-4(-16)(83)}}{2(-16)}[/tex]

Simplify:

[tex]\displaystyle x=\frac{-121\pm\sqrt{19953}}{-32}[/tex]

Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:

[tex]\displaystyle x=\frac{121\pm3\sqrt{2217}}{32}[/tex]

Therefore, our two solutions are:

[tex]\displaystyle x=\frac{121+3\sqrt{2217}}{32}\approx 8.20\text{ or } x=\frac{121-3\sqrt{2217}}{32}\approx -0.63[/tex]

Since time cannot be negative, we can ignore the second solution.

Therefore, the rocket will hit the ground after about 8.20 seconds.

I'LL GIVE YOU 5 STARES HELP. Find the area of the figures shown below and drop the correct result Into the appropriate blank. DRAG & DROP THE ANSWER 14 cm 55 cm 8 cm 11 36 m² 5 cm 38 cm 8 cm 58 cm 39 m2 8 m 40 m² 11 4 m 70 cm 10 m​

Answers

I saw its strength
It pushed and shoved
Moving spring into the past I felt its determination.
It talked with conviction,
Demanding control and respect I smelled its aroma.
It permeated the air,
Providing support and desire. I heard its voice.
It encouraged togetherness,
Allowing warmth to comfort us. I tasted its spirit.
It entertained the masses,
Generating newfound relationships. It woke me up,
Insisting I join the world.
It sheltered my fears,
Providing encouragement and hope.

Summer spoke to me.

How does the first–person perspective in the poem reinforce the idea that summer is an actual being?

a
It is omniscient, which means that it knows everything, so summer must be an actual being.
b
It allows the reader to get into summer's mind and experience what it experiences.
c
It is told from the perspective of summer, which proves that it is an actual being.
d
It gives the impression that the speaker personally encountered summer as an actual being.

hi, how can i graph the equation,

10i + 16p = t

?? thanks

Answers

Graph using a few selected points
Asymptotes: y=x/4, y=-x/4
Graph is inserted below :)

Help this is due in 2 minutes

Answers

b. Exponential decay.

HELP PLEASE.
Area=

If there is no value under the square root enter a 1.

Answers

10^2+16^2=100+256=356^2

The first box should be 2 and the second should be 356

I WILL NOT ACCEPT LINKS! AND WILL REPORT!!! Please help with this geometry question. An explanation would be nice!

Answers

ON=5.099  

Hope it helps

ANSWER CORRECTLY AND ILL MARK YOU AS BRAINIEST
Six containers have the following ounces in them: 6.2, 8.07, 9.4. 2.11, 5, 6.173 (Do not round your answer

Answers

Answer:

what is the question tho?

Answer:

Hi! The answer to your question is 36.953

Step-by-step explanation:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

3 3/4 x 4

Help me pas

Answers

Convert any mixed numbers to fractions.
Then your initial equation becomes:

15
4
×
4
1
Applying the fractions formula for multiplication,

=
15
×
4
4
×
1

=
60
4
Simplifying 60/4, the answer is
15

Answer:

15 (C)

//msg added cus it was short//

Solve for x. Use the photo for the chord

Answers

Answer: x=3

Step-by-step explanation:

work out the equation for each graph in the form
y=mx+c

please help !

Answers

Answer:

Top first one is y=-3x-3.

Step-by-step explanation:

I know you will be able to figure out the rest. I will explain. The problem if I just give you the answers are you won’t be actually able to solve it when you encounter it on like a test or something.

The explanation:

m=rise/run.

c=y intercept/ where it is on the y-axis.

if you go down on the y axis, it would negative. The opposite will be true if you go up.

I also think it is supposed to be y=Mx+b instead of y=Mx+c.

hopefully that made sense.

-4(-2)+(-12)÷(+3)+-20+(+4)+(-6)​

Answers

Answer:

-18

Step-by-step explanation:

[tex]-4(-2)+\frac{(-12)}{+3}-20+(+4)+(-6)=8-\frac{12}{3}-20+4-6=8-4-20+4-6=-18[/tex]

Answer:

-18

Step-by-step explanation:

-4(-2)+(-12)÷(+3)+-20+(+4)+(-6). [B.E.D.M.A.S rule] (First bracket)

= 8 - 12 ÷ 3 - 20 + 4 - 6. (Then division)

= 8 - 4 - 20 + 4 - 6. (Then after addition)

= 8 + 4 - 4 - 20 - 6

= 12 - 30. (At last subtraction)

= -18 (Ans)

Mrs Fuller plants a 4 inch tomato plant in her garden. The tomato plant grows at a rate of 2 inches each week. Which equation can be used to determine h, the height of the tomato plant in inches after w weeks?

Answers

Answer: 4 + 2w

Step-by-step explanation:

The height of the tomato plant in inches after w weeks will be the value of the current height plus the weekly growth pee week. This can be represented in an equation as:

h = 4 + 2(w)

h = 4 + 2w

For example, the height of the tomato plant in inches after 5 weeks will be:

h = 4 + 2w

h = 4 + 2(5)

h = 4 + 10

h = 14 inches

In a survey of 292 students, about 9.9% have attended more than one play. Which is closest to the number of students in the survey who have attended more than one play?​

Answers

Answer:

so sorry i needed the points to ask my question.

Step-by-step explanation:

30 Students I hope it helps.

Plzzzz asappp help thanks

Answers

Answer:

I might not be right but try following the steps in the screen shot

Also the answer is in the screenshot

Step-by-step explanation:

I tried my best. :>

solve for X
7x=49 (brainliest)

Answers

Answer:

7

Step-by-step explanation:

divide 7 to both side

7x/7=49/7

x=7

how to do this question plz answer me step by step plzz plz please​

Answers

Answer:

See the attached

Step-by-step explanation:

The solution and filled in Venn diagram is attached

What does the y-intercept represent in the graph below?​

Answers

It would be atleast 40,000

which is the correct input-output table for the function g(x)=-1/2(4x+6)

Answers

Answer: The third choice.

Step-by-step explanation: To find the first output, start with your first input. In this case, it's -2, so your equation would be g(-2)= -1/2(4(-2)+6). Start by solving inside the parenthesis. 4x-2=-8 and -8+6=-2. -1/2x-2= 1, so your first output should be 1. The only choice that has this is the third one, so that is your answer. Hope I could help :)


Note Figure is not drawn to scale.
If r= 2 cm and h = 2 cm, what is the surface area,
in terms of r?

Answers

Answer:

your answer is...

Step-by-step explanation:

50.265482457437

I used my calculator

which two ratios represent quantities that are proportional?

Answers

Answer:

C, because it equals in both sides

Answer:

The answer is C

Step-by-step explanation:

What's the domain and range of the exponential growth function? (please help asappp no spam please or links or anything like that!!! will give brainliest)

Domain: All real numbers; Range: All real numbers

Domain: x > –2; Range: y > –2

Domain: x < –2; Range: All real numbers

Domain: All real numbers; Range: y > –2

Answers

Answer:

Domain: All real numbers; Range: y > –2

Step-by-step explanation:

Asymptote is y = -2 so all y-values have to be greater than -2. The asymptote is horizontal so x-values can be all real numbers.

need help asap i have 25minutes left

Answers

bac=57

Step-by-step explanation:

lmk=50

abc= 63 (if they are parallel)

Question is in picture

Answers

Answer:

casino see  v

Step-by-step explanation:

j:)

A pattern of ordered pairs is shown.

(0, 1), (2,4), (4,7), (6, 10)

The pattern continues. What is the eighth ordered pair in the pattern?

A. (8,13) B. (14, 18). C. (14, 22) D. (16, 19)​

Answers

Answer: C

Step-by-step explanation:

X’s are going by +2 and y’s by +3

After identifying the pattern, its eighth ordered pair is: (14, 22), option C.

--------------------------

The ordered pairs given are: (0, 1), (2,4), (4,7), (6, 10)

From them, we can see that for each new ordered pair, x increases by 2, and y increases by 3.Thus, the next ordered pairs are: (8, 13), (10, 16), (12, 19), (14, 22).The eighth ordered pair is given by (14,22), option C.

A similar problem is given at https://brainly.com/question/16599038

PLEASE HELP ASAP ILL MARK BRAINLY IF U DO

Answers

Answer:

34.1 is the answer by Pythagoras thereom

Module 19 - Reflections
Assignment Active
Practice working with reflections.
Assignment
y
M(-5, 4)
M'(5, 4)
What is the rule for the reflection?
ry-axis(x, y) - (x, y)
P'y-axis(x, y) - (x,-y)
* rx-axis(x, y) (-x, y)
Orx-axis(x, y) = (x,-y)
2
L(-6,2)
N(-3,2)
N'(3,2)
L'(6,2)
x
-2
2
-2

Answers

Answer:

R y-axis (x,y) to (-x,y)

Step-by-step explanation:

The  rule for reflection is [tex]r_y[/tex] axis (x, y) -> (-x, y).

What is Transformation?

A transformation is a broad phrase covering four distinct methods of changing the shape and/or position of a point, line, or geometric figure.

The original shape of the object is known as the Pre-Image, and the final shape and location of the object is known as the Image during the transformation.

As per the figure. the coordinates of Triangle LMN are

L(-6, 2),

M(-5, 4)

N(-3, 2)

and, the coordinates of Triangle L'M'N' are

L'(6, 2),

M'(5, 4)

N'(3, 2)

Here, the y coordinate is same only the sign of x coordinate change.

So, the rule for reflection is r y- axis (x, y) -> (-x, y).

Learn more about Transformation here:

https://brainly.com/question/13801312

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Which of the following pairs of equations has (5, 3) as a solution?

Answers

Answer:

the last one .

Step-by-step explanation:

like my answer and brainliest please

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