what are the integer solutions to the inequality below?
[tex]3\leq 3x-4\ \textless \ 2x+1[/tex]

Answers

Answer 1

Given:

The compound inequality is:

[tex]3\leq 3x-4<2x+1[/tex]

To find:

The integer solutions for the given compound inequality.

Solution:

We have,

[tex]3\leq 3x-4<2x+1[/tex]

Case 1: [tex]3\leq 3x-4[/tex]

[tex]3+4\leq 3x[/tex]

[tex]\dfrac{7}{3}\leq x[/tex]

[tex]2.33...\leq x[/tex]             ...(i)

Case 2: [tex]3x-4<2x+1[/tex]

[tex]3x-2x<1+4[/tex]

[tex]x<5[/tex]                  ...(ii)

Using (i) and (ii), we get

[tex]2.33...<x<5[/tex]

The integer values which satisfy this inequality are only 3 and 4.

Therefore, the integer solutions to the given inequality are 3 and 4.


Related Questions

John and Paul both run on the same track each morning. The ratio of the number of miles John runs to the number of miles Paul runs is 5:8.

Answers

Answer:

Step-by-step explanation:

For example,

Solution: Finding a unit rate

If we divide 150 by 20, we get the unit rate for the ratio, 150 minutes for every 20 miles.

150÷20=7.5

So the runner is running 7.5 minutes per mile. We can multiply this unit rate by the number of miles:

7.5 minutes mile × 6 miles = 45 minutes

Thus it will take her 45 minutes to run 6 miles at this pace.

If it takes her 45 minutes to run 6 miles, it will take her 45÷3=15 minutes to run 6÷3=2 miles at the same pace.

If it takes her 15 minutes to run 2 miles, it will take her 4×15=60 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.

We found her pace in minutes per miles in part (a).

Josie is looking at buying a new phone for $800.If she does not want to pay the entire $800 she has the option of buying the phone for a $150 deposit and making 12 monthly payments of $75 each. If Josie chooses the payment plan what will be the percent increase on the original cost of the phone?

Answers

Answer:A 131.25%

Step-by-step explanation:

Can someone please help me answer this question asap thank you no links please thank you

Answers

Answer:

7 cm

24.5 cm

0.4 cm

69.91 cm

In UVW, u=51 inches,v= 61 inches and w= 62 inches.find the measure of angle V to the nearest degree

Answers

Answer:

49degrees

Step-by-step explanation:

Using the cosine rule

u² = v²+w²-2vwcosU

Substitute the given values

51² = 61²+62²-2(61)(62)cosU

2601 = 3721+3844-7564 cosU

2601 = 7565-7564cosU

-7564cosU = 2601-7565

-7564cosU = -4964

CosU =-4964/-7564

CosU = 0.6563

U = arccos(0.6563)

U = 49degrees(to nearest degree)

suppose the length of the pool in Example 1 is
3 times the width. How does the function that
represents the combined area of the pool and
the deck change?

Answers

do they have a picture which comes w it

how do you solve 5(-2x -3

Answers

Answer:

10x-15

Step-by-step explanation:

Step-by-step explanation:

-10x - 15

5 x -2x = -10x

5 x -3 = -15

(-9)5 ∙ (-9)7
what's the answer

Answers

Answer:

2835

Step-by-step explanation:

-9×5= -45

-9×7= -63

-45×(-63)=2835

A triangle has sides with lengths of 4 kilometers, 14 kilometers, and 16 kilometers. Is it a right triangle?

Answers

Answer:

Yes, it is

Hope this helped

Answer:

NO

Step-by-step explanation:

A right angle triangle will follow the PYTHAGORUS THEOREM. So the value found by adding the square of the two smaller sides should be same as the square of largest side.

1
1. You work full-time and make $17 per hour. What is your gross annual income?
A) $8160
B) $680
C) $35,360
D) $36,720

Answers

Answer:

C because if you make $17 dollars an hour that's 2,080 hours a year, Multiply that and you got C

You place four orders for 50 tennis rackets which cost $65 per racket you receive all 200 rackets there is a delivery charge of $15 per order what is your average cost per racket including delivery charges

Answers

Answer:

65.30

Step-by-step explanation:

1. 50x4=200

2. 200x65=13,000

3. 13,000 + (15x4)

4. 15 x 4 = 60

5. 13,000 + 60

6. 13,060/200 = 65.3

Your average cost per racket including delivery charges is $65.30.

First step is to calculate the cost of 200 rackets

Cost of 200 rackets= 200 ×$65

Cost of 200 rackets= $13,000

Second step is to calculate the total delivery fee

Total Delivery fee= 15 × 4

Total Delivery fee=$60

Third step is to calculate the total cost including delivery cost

Total cost including delivery cost=$13,000 + $60

Total cost including delivery cos = $13,060

Fourth step is to calculate the Average cost

Average cost per rackets=$13,060/200

Average cost per rackets=$65.30

Inconclusion the average cost per racket including delivery charges is $65.30.

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what is the general rule of the following geometric sequence

-4; -1; -1/4​

Answers

Answer:

Each of these numbers is divided by four to get the next number in the sequence, so the rule of this would be divide by 4.

Step-by-step explanation:

-4/4 is -1, -1/4 is -1/4 (negative one-fourth), and so on.

If AABC = APQR, then
AB =
Help please

Answers

Answer:

PQ should be the answer

Step-by-step explanation:

?% of $10 = $9
What is the percentage

Answers

Answer:

90%

Step-by-step explanation:

there are 100 % if you multiplied 10 by 10 you get that 100 % so multiply 9 by 10 to get 90 and that is your answer

Answer:

$90%

Step-by-step explanation:

90/100 *10.

9*1

$9%

Find the equation of the line
(Use exact numbers)

Y=___x+___
Please help

Answers

Answer: Y=2x+4

Step-by-step explanation:

1st step: Find the y-int ==> Y-int= 4

2nd step= To find the x-int go up 2 and go to the right 1 ==> 2/1=2

Y=2x+4

8 zombies have been spotted just outside of Galveston, its population by 50% each day. Write an equation that represents this specific outbreak.

Answers

Answer: 2+2?

Step-by-step explanation: Yes

(3x^2-2x+5)-(x^2+3x-2)•1/2x^2
In standard form?

Answers

Answer:

[tex]-\frac{1}{2} x^{4}-\frac{3}{2} x^{3} + 4x^{2} - 2x + 5[/tex]

PLS ANSWER! Dont put a link PLS ANSWER!!!!!!!!!!!

Answers

Answer:1) D 2) A 3)D and the last one is b

Step-by-step explanation:

PLEASE HELP ILL GIVE MORE IF ITS RIGHT

Answers

Answer:

choice 3) area = 1188 in²

Step-by-step explanation:

area = 36 x 33 = 1188 in ²

The line plot below shows the amount of water ( in gallons) students drank in a week. What is the difference in the lowest amount of water and the highest amount of water students drank

Answers

The difference in the lowest amount of water and the highest amount of water students drank is 1/2

How to determine the difference?

From the complete question (see attachment for line plot), we have:

Least = 1/8

Highest = 5/8

The difference is then calculated as:

Difference = Highest - Least

This gives

Difference = 5/8 - 1/8

Evaluate

Difference = 4/8

Simplify

Difference = 1/2

Hence, the difference in the lowest amount of water and the highest amount of water students drank is 1/2

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what is 22% of 64.82

Answers

Answer:

14.2604

Step-by-step explanation:

this is because 22% as a decimal would be 0.22, and since this is out of 64.82, you have to multiply 0.22 by 68.82

\\

Hope this helps <33

Answer:

14.2604

Step-by-step explanation:

[tex]64.82*.22=14.2604[/tex]

If
4x + y = 13
- y = 2
then y =

Answers

Answer:

y = 2

Step-by-step explanation:

-y = 2, that means y = opposite of 2, which is -2

Hope that helps! :)

4x + y = 13
- y = 2

y = -2

solve for the variable b -1/2 ( b - 6 ) =6

Answers

Answer:

56

Step-by-step explanation:

Answer:

b=6

Step-by-step explanation:

b-1/2(b-6)=6

b-1/2b+3=6

2b-b+6=12

b+6=12

b=12-6

b=6

For which value of is the following number undefined


x - 3 / x + 4

Answers

Answer:4x - 2 = 3x + 1

Step-by-step explanation: shooooooooo papi

Answer:

x = - 4

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make it undefined.

Equating the denominator to zero and solving gives the value that x cannot be, that is

x + 4 = 0 ⇒ x = - 4

Thus x = - 4 is the excluded value

Suppose quadrilateral ABCD is a square and the slope of BC is -n. What is the slope of AB?

Answers

Answer:

-p?

Step-by-step explanation:

Fran withdrew 6.4% of her savings account to put towards the purchase of a new car. If she put $2,400 down on her car, what was her savings account balance before she withdrew the money?

Answers

Answer:

$3,550 dollars

Step-by-step explanation:

6.4% off savings

- a total of $2,400

The percentage is that indicating the hundredth total amount in the saving account before withdrawing such that 6.4% of that is $2400 is $37500.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Let's suppose the total amount of money before withdrawing x.

It is known that x% of y is given as, (x/100)y.

Therefore,6.4% of x is (6.4/100)x = 0.064x

The 6.4% of the x is 2400

So, 0.064x = 2400

x = 2400/0.064 = $37500

Hence "The percentage is that indicating the hundredth total amount in the saving account before withdrawing such that 6.4% of that is $2400 is $37500.".

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Given m||n, find the value of x. (5x-23)° (7x-1)°​

Answers

Answer:

X=17

Step-by-step explanation:

5x-23+7x-1=180

12x=180+24

12x=204

x=17

Please help me picture below ! No links

Answers

Answer:

nine decided by three is three and three times three is nine so ur answer is three

what is the missing blank?

Answers

Answer:

<1 and <8 are alternate exterior angles

Step-by-step explanation:

Alternate means on the opposite side of the transversal

Exterior means outside the parallel lines

<1 and <8 are alternate exterior angles

Which number is an integer?

Answers

Answer:

Step-by-step explanation:

Can you please specify on that question

Answer:

Integers are numbers that include the negatives, zero and positives.

Step-by-step explanation:

If you ever get confused there's a big circle chart to help you remember look for it online!! What I use to remember is visualizing a number line!

First is the real numbers, so the numbers we were taught since we were little like 1, 2 ,3, 4, 5, 6 and so on. So that's the first part of the number line.

Next is the whole numbers so you just add a zero to that number line. Whole numbers is just all of the real numbers + the number zero.

Then it's the integers so you add the left side of that number line. Integers are real numbers, whole numbers, and negatives. So basically on the number line it's the negatives , zero, and the positives.

Last it's the radicals so all parts of a number like fractions and decimals. So you can add .5 in between the numbers of that numberline.

I hope this strategy helped and if it didn't here's that circle chart!!

I really hope this did help tho!!

Can someone please help me with math. Pls don't take my points.

Answers

Answer:

0.09

0.16

0.35

0.65

0.19

0.56

Step-by-step explanation:

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