Solve:||x-3|-2|≤1
Please show work!
Thanks

Answers

Answer 1

Answer:

Step-by-step explanation:

Hello,

We know that

[tex]|x|=\begin{cases}x & \text{if } x\geq 0 \\ -x & \text{if } x<0 \end{cases}[/tex]

So we need to take into account two cases

Case 1 - [tex]x-3\geq 0<=> x\geq 3[/tex]

Then, |x-3|=x-3

||x-3|-2|=|x-3-2|=|x-5|

Either x-5 is positive and then |x-5|=x-5 and

[tex]|x-5|\leq 1<=>x-5\leq 1<=>x\leq 6[/tex]

Or x-5 is negative and then, |x-5|=-x+5

[tex]|x-5|\leq 1<=>-x+5\leq 1<=>4\leq x[/tex]

So the solution is [4;6]

Case 2 - [tex]x-3< 0<=> x< 3[/tex]

Then, |x-3|=-x+3

||x-3|-2|=|-x+3-2|=|-x+1|

Either -x+1 is positive and then |-x+1|=-x+1 and

[tex]|-x+1|\leq 1<=>-x+1\leq 1<=>0\leq x[/tex]

Or -x+1 is negative and then, |-x+1|=x-1

[tex]|-x+1|\leq 1<=>x-1\leq 1<=>x\leq 2[/tex]

So the solution is [0;2]

Conclusion

The solution is [0;2]∪[4;6]

Thanks


Related Questions

Dan drove his truck 2436 miles in six months at that rate how far will he drive in 12 months

Answers

Answer:

4,872 miles

Step-by-step explanation:

Step 1:

2,436 : 6

Step 2:

2,436 : 6 = x : 12

Step 3:

6x = 29,232

Answer:

x = 4,872

Hope This Helps :)

Use completing the square to solve for x in the equation (x + 7) (x minus 9) = 25.

Answers

Answer:

x=1+/- the square root of 89

Answer:

x=1+ (square root of 89)

Step-by-step explanation:

​Kirk's goal was to save​ $300 for a trip. In the first​ week, Kirk saved​ $16 from his allowance and​ $54 from his job. He spent​ $5 for lunch one day and another​ $2 on the bus. The second​ week, Kirk saved​ $62 and another​ $41 but spent​ $2 for the bus and​ $4 for lunch. How much money did Kirk save after 2​ weeks? Choose the correct answer below and fill in the answer box to complete your choice.

Answers

Answer:

160 dollars.

Step-by-step explanation:

16+54= 70

5+2=7

70-7=63

62+41=103

2+4=6

103-6=97

97+63=160

Hope this helps! ^^

Answer:

║Ф║Hello Person!║Ф║

Your answer should be:

460

300+16+54-5-2+62+41-2-4= 460

Step-by-step explanation:

Δ I hope this helped you! Δ

(I would appreciate a brainliest!)

║∅║Thanks for your time!║∅║

Choose the appropriate descriptor for the term gram. mass volume length area

Answers

Answer:

Mass is the appropriate term.

Step-by-step explanation:

how to solve the equation 2= -9n +22-n

Answers

Answer:

n = 2

Step-by-step explanation:

2 - 22 = -9n + 22 - n - 22

-20 = -9n - n

-20 = -10n

-20/-10 = -10/-10n

-2 = -n

n = 2

Answer:

The value of n is 2.

Step-by-step explanation:

First, you have to collect like-terms :

[tex]2 = - 9n + 22 - n[/tex]

[tex]2 = - 10n + 22[/tex]

Next, you have to subtract 22 on both sides :

[tex]2 - 22 = - 10n + 22 - 22[/tex]

[tex] - 20 = - 10n[/tex]

Lastly, have to divide -10 on both sides :

[tex] - 10n = - 20[/tex]

[tex] - 10n \div - 10 = - 20 \div - 10[/tex]

[tex]n = 2[/tex]

可二人十
Help solve this problem

Answers

Hi! This is my first time helping someone so I hope this helps!

X=1
Y=5

First in the first equation, subtract x on both sides.

Y= 6-x

Then substitute that into the second equation.

-3x + 6-x = 2

-4x + 6= 2

-4x = -4

x= 1

Substitute it to the first equation

Y= 6-1

Y= 5

X= 1

Hope this helps. I hope you have a great day!

What multiplication fact can help you find 7/7

Answers

Answer:

The rule of Identity. X*1=X.

Divide both sides by x, and you get

X/X = 1

The length of AB = in ?

Answers

AB = 2.894 inches

hope this helps

What is a y-intercept of the continuous function in the table?

Answers

Answer:

5=y-intercept

Step-by-step explanation:

the y intercept point is when y has a number but x is 0 so we see what is y (f(x)) and it is 5

Simplify: 6 (4x - 5)

Answers

Answer:

=24x−30

Step-by-step explanation:

=(6)(4x+−5)

=(6)(4x)+(6)(−5)

=24x−30

Answer:

6 (4x - 5)

24x -30

i think question is not complete

Step-by-step explanation:

Simplify 6(1/4+5/2)-2

Answers

6(0.25+2.5)-2
6(2.75)-2
16.5-2
=14.5

Answer:

14 1/2 or 29/2

Find the midpoint of points A(-3,9) and B(0, 1) graphically.


Answers

Answer:

[tex](-\frac{3}{2} , 5)[/tex]

Step-by-step explanation:

The graph is in the image

[tex]Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-3,\:9\right),\:\left(x_2,\:y_2\right)=\left(0,\:1\right)\\\\\left(\frac{0-3}{2},\:\frac{1+9}{2}\right)\\\\Add\:or\:subtract\:the\:numbers\\\\(\frac{-3}{2} , \frac{10}{2}) \\\\Simplify\\\\(-\frac{3}{2} , 5)\\[/tex]

The gestation period of humans (266 days) is what percent longer than the gestation period of pigs (115 days).

Answers

Answer:

56.8%

Step-by-step explanation:

(115/266)* 100 = 43.2%

which means 115 is 43.2% of 266

so,

The gestation period for Humans is 56.8% (100 - 43.2) longer than of pigs

I hope this is correct!

What are the coordinates of the image of (- 4, 5) under the translation (x,y) (x-3,y+5)

Answers

(-4-3) (5+5) = -7,10

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Answers

Answer:

y = 1/2x - 4

Step-by-step explanation:

You would use point slope to solve this. y-y = m(x-x) with your numbers it would look like this ---> y+3 = 1/2(x-2). (I changed it to +3 because y- -3 = y+3. Two negatives make a positive.)  Next you would use the distributive property and it would look like this ---> y+3 = 1/2x - 1 -----> -3 on both sides ------->

y = 1/2x - 4. Hope this helped!!!!

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Answers

Answer:

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed

Four hundred seven million eighty two thousand in numbers

Answers

Answer:

407082000

Step-by-step explanation:

hope it helps

Pls mark as brainiest...........

Answer:

407,820,000.

Step-by-step explanation:

This is how four hundred seven million eighty two thousand is written a numerical value.

xy given x=3/5 and y= -3/4

Answers

Answer:

-9/20

Step-by-step explanation:

xy

Let x=3/5 and y= -3/4

3/5 * -3/4

-9/20

Answer: -9/20

Step-by-step explanation: xy means x times y, so all you need to do is substatute 3/5 in for x and -3/4 in for y multiply numerators times numerators and denominators times denominators.

How can i solve to find AB?

Answers

Answer:

17

Step-by-step explanation:

AB + BC = AC.

Therefore,

[tex](3x+2)+(5x+7)=49[/tex]

Remove brackets:

[tex]3x+2+5x+7=49[/tex]

Add up terms:

[tex]8x+9=49[/tex]

Subtract 9 from both sides:

[tex]8x+9-9=49-9[/tex]

[tex]8x=40[/tex]

Divide both sides by 8:

[tex]\frac{8x}{8}=\frac{40}{8}[/tex]

[tex]x=5[/tex]

----------

[tex]AB=3x+2=3(5)+2=15+2=17[/tex]

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y=1x

y = x2


y = x + 2


y=12x

Answers

Y=1x because if you draw it on the line you’ll see the linear variation

The measure of angle

Answers

Answer:
120 degrees

Explanation:
Opposite angles (angles that are on opposite sides of an intersection) are equal to each other. Because angle 2 and 120 degrees are opposite angles, angle 2 is equal to 120 degrees.

I hope this helped if it did, a brainliest would be much appreciated:)

An object is translated by (x - 2; y- 6). If one point in the pre-image has the coordinates (-3, 7), what would be the
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(-5,1)
(-1, 13)
(-1,7)
(-9,5)

Answers

Answer:

(-5,1) would be the coordinates of its image

Answer:

(5,1)

Step-by-step explanation:

hope this helps

In 35 divided by 5, 5 is the dividend, quotient, or divisor

Answers

Answer:

Divisor

Step-by-step explanation:

Which is bigger 6.8" or 6.52"

Answers

Answer:

6.8 is bigger than 6.52

6.8 is bigger than 6.52

Name (Templatel 09.09.2020 - Assignment 004 NAME Assignment 004 - Dividing Fra Divide Fraction by Fraction Divide. Write in simplest form. 2/3÷4/5​

Answers

Answer:

5/6

Step-by-step explanation:

2/3 ÷ 4/5​

2/3 × 5/4

10/12

5/6

The sum of three consecutive integers is 267. What is the largest integer?

Answers

Answer:

let integers be x,2x, 3x respectively

x+2x+3x= 267

6x= 267

x=267/6= 44.5

2x= 44.5*2= 89

3x= 44.5*3= 133.5

largest integer = 133.5

hope it helps

plz mark as brainliest

1. Four times a number increased by 3 is -89. what is the correct equation?!? PLEASE HELP ME!!!
A. 3+= 89
C. 4n+3 = -89
B. 4n-3= -89
D.4+3n = -89

Answers

I would assume it’s C

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Answers

he was at the end of the day with u and I 6so was a little bit of a joke but I 6

Step-by-step explanation:

just like that I don't think you know that I have to do that again 261and but it 1was 1is 1and 1is 1and is not 774a

A car rental business charges a daily fee along with a one-time fixed charge to refuel the car when it is returned. The equation the business uses to calculate the total rental cost, c is c=15d+24c = 15 d + 24, where d represents the number of rental days. What is the daily increase in the total cost of the rental?

Answers

Answer:

$15

Step-by-step explanation:

Since we are given the actual equation, which is c = 15d + 24 (it is repeated in the question twice) we can see that the independent variable would be the number of days that the car is rented. Therefore we can simply plug in a value for this to calculate c. So below we can see the total cost for 1 day rent (d = 1 ) and 2 days rented (d = 2)

c = 15(1) + 24 = 39

c = 15(2) + 24 = 54

Now we can simply subtract these two values and to see the daily increase

54-39 = 15

Therefore we can see that the total price will increase by $15 for each day that it is rented.

What is 10% of 344?

Answers

Answer:

34.4

Step-by-step explanation:

10% is the same thing as 0.1 so 344 times 0.1 is 34.4

A percent (%) is equal to 1/100 (We actually don't call that 'per''cent' for no reason)

So 10% is actually 10 times % which is:

[tex]10\% \\ 10(\frac{1}{100}) \\ \frac{10}{100} \\ \frac{1}{10}[/tex]

If you get a calculator and calculate 1/10 the calculator should give 0.1

You might be taught that to get the decimal form from percent you just move the decimal point to the left twice (like 34% -----> .34) but if you do this, you are essentially dividing by 100 or multiplying by 1/100

now you know 10% is 0.1 the next thing to do is multiply it to 344.

[tex]344(\frac{1}{10}) \\ \frac{344}{10} \\ 34.4[/tex]

Answer:

34.4

Step-by-step explanation:

344 x 1/10 = 34.4

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