Compare solving equations using addition with solving inequalities using addition

Answers

Answer 1

Answer:

give picture

Step-by-step explanation:

Answer 2

Solving inequalities with addition is similar to solving equations with addition in the initial steps, but it differs in the final answer due to the inequality sign. In both cases, you use addition to isolate the variable. However, with inequalities, you must consider the direction of the sign throughout the process.

When solving inequalities with addition, like equations, the goal is to isolate the variable on one side. You use addition to simplify the expression. Begin by treating the inequality like an equation, adding or subtracting the same value to both sides to eliminate constants and isolate the variable.

For example, if you have [tex]\(2x + 5 > 10\)[/tex], subtract 5 from both sides to get [tex]\(2x > 5\)[/tex].

Here's where it diverges: since inequalities involve the relationship between two quantities, you need to be mindful of the inequality sign. When you multiply or divide both sides by a negative number, the inequality direction flips.

For example, if you multiply [tex]\(x < 3\)[/tex] by -2, the sign changes to [tex]\(x > -6\)[/tex].

Remember, you're looking for a range of values that satisfy the inequality. So, when representing your final answer, use the appropriate inequality sign. For instance, if [tex]\(3x + 2 \leq 8\)[/tex], after simplifying, you'll have [tex]\(x \leq 2\)[/tex], indicating that any value of [tex]\(x\)[/tex] less than or equal to 2 satisfies the inequality.

In summary, while solving inequalities with addition is akin to solving equations with addition in the initial steps, the crucial distinction lies in managing the inequality sign throughout the process and representing the solution as a range of values that satisfy the inequality.

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Complete Question:

How is solving inequalities with addition is similar to or different from solving equations with addition ?


Related Questions

8z + 6 = 7z + 4
I need help with it please show the steps

Answers

z=2 thats the answer to your problem

Can someone help me with number 8 :(

Answers

Answer:

a1=5

d=9-5=4

a20=5+19×4=81

Can someone plsss help me with the 2 one

Answers

Answer: [tex]\sqrt{73}[/tex] for number 7

Step-by-step explanation:

a²+b²=c²

3²+8²=c²

9+64=c²

[tex]\sqrt{73}=\sqrt{c^2}\\\sqrt{73}=c[/tex]

3over 7 = blank over 35

Answers

Let blank be x

[tex]\\ \sf\longmapsto \dfrac{3}{7}=\dfrac{x}{35}[/tex]

[tex]\\ \sf\longmapsto 7x=35(3)=105[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{105}{7}[/tex]

[tex]\\ \sf\longmapsto x=15[/tex]

PLEASE HELP!!
(04.03)
Given the function g(x) = 5(2)^x, compare the average rate of change from x = 1 to x = 2 and from x = 3 to x = 4.
How many times greater is the average rate of change from x=3 to x=4 than from x=1 to x=2?
О 4 times
O 5 times
O 2 times
O The average rate of change of Section B is not greater than the average rate of change of Section A.

Answers

Answer:  Choice A.   4 times

========================================================

Explanation:

We'll be using this formula

[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]

to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).

To start things off, we'll compute the AROC from x = 1 to x = 2.

[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\[/tex]

Do the same for the AROC from x = 3 to x = 4.

[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\[/tex]

The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.

Write a unit rate for each situation . 20$ saved in 4 weeks

Answers

Answer:

so the answer is 5

Step-by-step explanation:

20/4=5

Find the upper quartile for the data. {9, 6, 13, 8, 8, 10, 9.5, 8, 7.5, 8.5}
A. 9
B. 9.5
C. 10
D. 8.5

Answers

Answer:

the answer is 9.5 (B)

Step-by-step explanation:

george is building a fence at a consent rate of 1/3 section of fence every 1/2 hour at the rate. what fraction represents the section iof fence george can build per hour

Answers

George, after 1 hour, Should have 2/3 section of fence done. Since there is 30 minutes 1/2 an hour, And he is doing 1/3 every 30 minutes. You must add 1/3 and 1/3 to get an hours worth of work

A 144-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
The shorter piece is inches long.

Answers

Answer:

shorter piece is 28.8 inches

Step-by-step explanation:

Answer28.8

Step-by-step explanation:

28.8 x 5 = 144

Someone help me I will mark you as brain

Answers

Answer:

- 1

Step-by-step explanation:

-3 (-3) -10

9 - 10 = -1

a³-a²b-ab²+b³hihihihihihihi

Answers

Refer to the attachment
a³ + b³ = (a + b)(a² – ab + b²)

help me with this please

Answers

Answer: 65

Step-by-step explanation:

Find the EQUATION of the line through (-10,-12) and (-15,3). Use the form y=mx+b.​

Answers

Y=Mx+b

Y=-3x-42

Please mark brainliest. Thank you

pls help ASAPPPP11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

It's between 0 and 1

Step-by-step explanation:

1/64 = 0.015625

hi pls help me thanksss
pls provide me with workings thankss :)​

Answers

Step-by-step explanation:

(i)

Using cos(a - b) = cos a cos b + sin a sin b

[tex]\frac{4}{5}[/tex] = cos a cos b + [tex]\frac{1}{5}[/tex]

cos a cos b = [tex]\frac{4}{5} -\frac{1}{5} = \frac{3}{5}[/tex]

(ii)

Using cos(a + b) = cos a cos b - sin a sin b

cos(a + b) = [tex]\frac{3}{5}-\frac{1}{5}=\frac{2}{5}[/tex]

(iii)

Using cot a = [tex]\frac{cos a}{sin a}[/tex]

[tex]=(\frac{cos A}{sin A} )(\frac{cos B}{sin B} )[/tex]

[tex]=\frac{cos A cos B}{sin A sin B}[/tex]

[tex]=\frac{\frac{3}{5} }{\frac{1}{5} }[/tex]  [tex]=\frac{3}{5}[/tex] × [tex]5[/tex]

= 3

please give me a brainliest answer

triangular field having the length of sides are 42m, 34m and 20m respectively. find the area of the field (need this answ with full explanation) ​

Answers

Answer:

[tex]A = 336[/tex] [tex]m^{2}[/tex]

Step-by-step explanation:

Using the formulas

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]s=\frac{a+b+c}{2}[/tex]

Solving for [tex]A[/tex]

[tex]A=\frac{1}{4} \sqrt{-a^{4}+2(ab)^{2} +2(ac)^{2} -b^{4} +2(bc)^{2}-c^{4} }[/tex]

[tex]=\frac{1}{4} *\sqrt{-42^{4} +2*(42*34)^{2}+2*(42*20)^{2} -34^{4} +2*(34*20)^{2} -20^{4} }[/tex]

[tex]=336m^{2}[/tex]

Answer:

✌ just because that what the answer is I just know it cuz im right

Solve for x
please give an explanation

Answers

[tex]293 {8}^{?} \sqrt{96} [/tex]

The perimeter of a triangle is 65 cm. The
lengths of the sides are x cm, x+8 cm, and
X+ 12 cm.
What is the length, in cm, of the longest side of
the triangle?

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The longest side measures :

[tex]27\: \: cm[/tex]

[tex] \large \boxed{ \mathfrak{Explanation}}[/tex]

Perimeter of a triangle is equal to sum of measures of its all three sides, that is :

[tex]x + x + 8 + x + 12[/tex]

and according to the question, the perimeter of the triangle is = 65 cm

so, let's equate both the expressions to find value of x :

[tex]x + x + 8 + x + 12 = 65[/tex][tex]3x + 20 = 65[/tex][tex]3x = 65 - 20[/tex][tex]3x = 45[/tex][tex]x = 45 \div 3[/tex][tex]x = 15[/tex]

The longest side of the Triangle is :

[tex]x + 12[/tex][tex]15 + 12[/tex][tex]27 \: \: cm[/tex]

27cm

Step-by-step explanation:

(xcm) + (x+8cm) + ( x+ 12cm) = 65cm

Open Bracket

xcm + x+8cm + x+12cm = 65cm

3x+ 20cm = 65cm

Collect like terms

3x = 65cm - 20cm

3x = 45cm

Divide both sides by 3

3x/3 = 45cm/3

x = 15cm

The longest side of the triangle =( x+12cm)

= (15+12)cm= 27cm

1/5 divided by 2/3 help meee loll

Answers

Answer:

3/10 or 0.3

Hope this helps

the awnser is 0.3 .......................

Classify the quotient as​ positive, negative,​ or zero - 25 ÷ - 5

Answers

Answer:

-25÷-5= 5 The quotent is positive.

Step-by-step explanation:

positive+positive=positive

negative+negative= positive

positive+negative=negative

negative+positive=negative

The ratio of men to women working for a company is 4 to 5. If there are 110 women working for the company, what is the total number of employees?

Answers

Answer:

198

Step-by-step explanation:

?/4        110/5

cross-multiply 4*110

440

divide 440/5

88 men

add total employees

110 women + 88 men = 198

plz help answer the following questions

Answers

I would but image posted is very blurry


Item 1
What is the slope of the line on the graph?


WORTH 20 POINTS
Enter your answer in the box.

Answers

Answer:

-2

Step-by-step explanation:

Hope it helps

An investor invests $525 in stock. For each month following, the stock increased at a rate of $25 per
month
Identify the slope of the linear relationship. Explain what the slope represents in the context of the
problem
• identify the y-intercept of the linear relationship. Explain what the y-intercept represents in the
context of the problem.
Create a model/build the function/write the equation in slope-intercept form to represent the total
value of the stock, f (2), based on the number of months, I.

Answers

Answer: f(x) = mx+ b

slope = m = $25 / month

This means that for every month (x) that goes by, the total value of the stock (f(x)) will increase by $25.

y-intercept = b = $525

This is the amount of money in the account at time = 0. This will be equal to the original investment of $525.

f(x) = mx+ b = 25x + 525

Step-by-step explanation:

Help lolz- Acellus Write 0.34 as a fraction using the steps below

Answers

Answer:

Step-by-step explanation:

3.1x10 = 31, and 9x10=90, so the fraction is 31/90, whcih equals 3.44444444 . . .

A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price of $66, while 10000 shirts can be sold at a price of $48. Give a linear equation in the form p

Answers

Answer: p = [tex]\frac{-n}{500} +68[/tex]

Step-by-step explanation:

Let n represent the number of shirts and p represent the price, the there is a linear relationship between n and p, then the model equation is given as:

p = mn + b, where

m = slope and b is the intercept

From the question, when n = 1000, p = $66

And, when n = 10,000 , p = $48

The formula for finding slope is given as:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

[tex]y_{1} = 66[/tex]

[tex]y_{2} = 48[/tex]

[tex]x_{1} = 1000[/tex]

[tex]x_{2} = 10000[/tex]

substituting the values,

m = [tex]\frac{48-66}{10000-1000}[/tex]

m = [tex]\frac{-18}{9000}[/tex]

m = [tex]\frac{-2}{1000}[/tex]

m = [tex]\frac{-1}{500}[/tex]

The linear equation thus becomes

p = [tex]\frac{-n}{500}+b[/tex]

To find the value of b, substitute  p = 66 and n =1000 into the equation

That is,

66 = [tex]\frac{-1000}{500}+b[/tex]

66 = -2 + b

68 = b

Therefore b = 68

The linear equation is therefore

p = [tex]\frac{-n}{500} +68[/tex]

Hi I really need help with this question, ANSWERS ONLY, I'll give 35 POINTS, PLEASE

What is the positive conterminal angle to -32° that is between 500° and 1000° and a negative conterminal angle to -32° that is between -500° and -50°?

positive coterminal angle:

negative coterminal angle:

Answers

Answer:

0° and 90°, it's Ql. If between 90° and 1800 QQ. ... Find a positive and a negative conterminal angle for the given angle.

Step-by-step explanation:

The positive and negative coterminal angles to -32° are:

Positive coterminal angle = 688°

Negative coterminal angle = -392°

What is a coterminal angle?

Coterminal angles are those whose terminal sides and beginning sides coincide.

The given angle measure is -32°.

The positive coterminal angle is:

-32° + 360°

= 328°

Since the angle is not between 500° and 1000°, add 360° one more times:

328° + 360°

= 688°

The negative co-terminal angle is:

-32° - 360°

= -392°

Hence, the positive and negative coterminal angles to -32° are:

Positive coterminal angle = 688°

Negative coterminal angle = -392°

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I WILL GIVE YOU BRAINYIST IF YOU ANSWER THIS FOR ME

Answers

Answer:

A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

A city bus goes 18miles in 30 minutes . HOW far does it go in 2 minutes?

Answers

the bus goes 9 miles every 2 minutes

Answer:

the city bus would cover 6 miles in 10 minutes.

Step-by-step explanation:

18 miles = 30 minutes

? miles = 10 minutes

cross multiply

? x 30 = 18 x 10 (180)

? = 180/30

? = 6

the city bus would cover 6 miles in 10 minutes.

In a student president race student A received 9 votes received by student B if student A received 540 votes, how many votes did student B receive?

Answers

Answer: 60 Votes

Step-by-step explanation:

540 divded by 9 which equals 60 votes.

So Student B received 60 votes.

60 votes was received by student B.

540/9=60

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