It looks like the inequality is
[tex]\bigg|x + 6 - |3x + 6|\bigg| + |x + 2| - x - 4 \le 0[/tex]
or equivalently,
[tex]\bigg|x + 6 - 3 |x + 2|\bigg| + |x + 2| - x - 4 \le 0[/tex]
Recall the definition of absolute value:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
By this definition, we have
[tex]|x + 2| = \begin{cases} x + 2 & \text{if } x + 2 \ge 0 \\ -(x + 2) & \text{if } x + 2 < 0 \end{cases} = \begin{cases} x + 2 & \text{if } x \ge -2 \\ -x - 2 & \text{if } x < -2 \end{cases}[/tex]
Suppose [tex]x < -2[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (-x - 2)| + (-x - 2) - x - 4 \\\\ = |4x + 12| - 2x - 6[/tex]
By definition of absolute value,
[tex]|4x + 12| = 4 |x + 3| = \begin{cases} 4x + 12 & \text{if } x \ge -3 \\ -4x - 12 & \text{if } x < -3 \end{cases}[/tex]
so we further suppose that [tex]x < -3[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (-4x - 12) - 2x - 6 \\\\ = -6x - 18 \le 0 \\\\ \implies x \ge -3[/tex]
but this is a contradiction, so this case gives no solution.
If instead we have [tex]-3 \le x < -2[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |4x + 12| - 2x - 6 \\\\ = (4x + 12) - 2x - 6 \\\\ = 2x + 6 \le 0 \\\\ \implies x \le -3[/tex]
and [tex]-3 \le x[/tex] and [tex]x \le -3[/tex] means that [tex]\boxed{x = -3}[/tex].
Now suppose [tex]x \ge -2[/tex]. Then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = |x + 6 - 3 (x + 2)| + (x + 2) - x - 4 \\\\ = |-2x| - 2 \\\\ = 2 |x| - 2[/tex]
If we further suppose that [tex]-2 \le x < 0[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = -2x - 2 \le 0 \\\\ \implies x \ge -1[/tex]
Otherwise, if [tex]x \ge 0[/tex], then
[tex]\bigg| x + 6 - |3x + 6| \bigg| + |x + 2| - x - 4 \\\\ = 2 |x| - 2 \\\\ = 2x - 2 \le 0 \\\\ \implies x \le 1[/tex]
Taken together, this case gives the solution [tex]\boxed{-1 \le x \le 1}[/tex]
So, the overall solution to the inequality is the set
[tex]\boxed{\left\{ x \in \mathbb R : x = -3 \text{ or } -1 \le x \le -1 \right\}}[/tex]
16. Read the bar graph and answer the following questions
(1) What is the information given by the bar graph?
(ii) How many tickets of Assam State Lottery were sold by the agent?
(ii) of which state, were the maximum number of tickets sold?
Answer:
Hope it helps!!!!!!Brainliest pls!!!!!!!16.
.
What is the sum of the geometric series Σ2
Σ(3)
rounded to the nearest whole number?
(1 point)
χ 0
O4
Ο0
O2
O3
What is the sum of the geometric series Σ2
Σ(3)
rounded to the nearest whole number?
Answer: O2
I can’t seem to get the answer right. What is log 10000?
Answer:
[tex]log(10000) = 4[/tex]
Step-by-step explanation:
Count the number of zeros, if it's a perfect power of 10. :)
Answer:
the answer is for
Step-by-step explanation:
have a great day
Please Help!
The graph shows the vertical displacement y, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds, x.
From its resting position, how long does it take the weight to bounce one direction, then the other, and then return to its resting position?
-3s
-6s
-16s or
-32s
It would take 6 seconds for the weight to bounce one direction, then the other, and then return to its resting position
What is a periodic function?
A periodic function is a function that repeats itself at regular intervals. The period of this function is the time taken to complete one oscillation while the amplitude is the distance from the origin to peak.
From the diagram:
Time taken for the weight to bounce one direction, then the other, and then return to its resting position = 7.5s - 1.5 s = 6 s
It would take 6 seconds for the weight to bounce one direction, then the other, and then return to its resting position
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pls helpp !
During a sale, a store offered a 15% discount on a bed that originally sold for
$350. After the sale, the discounted price of the bed was marked up by 15%.
To the nearest whole number, what percent of the original price was the price
after markup?
Answer:
342
Step-by-step explanation:
85% of 350 is 297.5, 115% of 297.5 is 342.125
WHAT TIME IS TWENTY FIVE TO EIGHTT???
Answer:
7:35
Step-by-step explanation:
60 minutes in an hour, 25 minutes back from 8:00 is 7:35, 35+25=60
What are the sales taxes on the state level collected for
Answer:
The goverment collects sales taxes so they can use the moeny to pay for services like police, firemen, hospitals. They also use them to pay for building things like roads, puplic schools, puplic outdoor places, and building
Step-by-step explanation:
Please use an equation step by step and please show the numbers do not use words
Answer:
What's the question????
Step-by-step explanation:
help someone help me pls
can somebody help me with 6 and 7 and show the work for it? thank you
Answer:
Answer For Number 6 is $30
Step-by-step explanation:
We can find how much molly would save by first finding out how much 20% of $275 is. We can do that by multiplying 275 by 0.20 since 0.20 is 20% in decimal form
[tex]275*0.20 = 55[/tex]
Now that we know 20% of 275, we can find the price of the microwave at store B by subtracting 55 from the original price.
[tex]275 - 55=220[/tex]
Now we can find how much Molly would save by subtracting our discounted price from the price of the microwave from store A
[tex]250-220=30[/tex]
Hence, the amount she would save is $30
PLEASE HELP PLEASE HELPPP
Answer:
40
Step-by-step explanation:
The LCM is forty.
PLEASE MARK AS BRAINLIEST!
Answer:
40
Step-by-step explanation:
2/5 = 16/40
1/8 = 5/40
Find the difference equation
Y= a / x +b
Answer:
y+a+x=b
Step-by-step explanation:
hope it's work ty make me brainless tyy
The are 3 blue marbles, 4 red marbles and 2 yellow marbles. Find the ratio of blue marbles to red and yellow marbles. options:
A 1:2
B 3: 4
C 3: 2
D 4:3
Answer:
1:2
Step-by-step explanation:
The ratio unsimplified of blue marbles to red and yellow is 3:6, but since both numbers in the ratio can be divided by 3, we can simplify the ratio to 1:2.
Last year, there were b pies baked for the bake sale. This year, there were 235 pies baked. Using b, write an expression for
the total number of pies baked in the two years.
Answer:
235+b
Step-by-step explanation:
I may not have understood this, but I don't know where the confusion is?
What is 43 percent as a decimal and a fraction?
43
%
is
43
100
, so move the decimal
2
places.
43
becomes
.43
.
Answer:
decimal: 0.44, Fraction: 43/100
Step-by-step explanation:
I need help
At olive garden Emily’s food costs $25.67 in total. If she left a 15% tip to the waitress, how much did Emily pay in total?
Answer:
The answer is $29.52
Step-by-step explanation:
25.67*.15=3.85
25.67+3.85=29.52
The table shows the purchases made by two customers at a meat counter. You want to buy 2 pounds of sliced ham and 3 pounds of sliced turkey. Can you determine how much you will pay? Explain.
Answer:
No
Step-by-step explanation:
The equations have infinitely many solutions, so you cannot determine the cost of each meat.
You want to buy 2 pounds of sliced ham and 3 pounds of sliced turkey.
We can not determine the amount you will pay.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
The table shows the purchases made by two customers at a meat counter.
Let x represents the weight of a sliced turkey and y be the weight of a Sliced ham.
Now, we have a system of equations,
0.5x + y = 8.5 {equation 1}
2x + 4y = 34 {equation 2}
Simplify,
x + 2y = 17
Divide by 4, we get,
0.5x + y = 8.5
That means, the lines are the same.
So, there are infinitely many solutions possible.
Therefore, there are infinitely many solutions possible.
To learn more about the system of equation;
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Candy is paving a narrow pathway with pebbles. She needs 100 pebbles for each four feet of path. How many feet can she pave if she has 525 pebbles?
express the ratio below in its simplest form.3:12:9
Answer:
Step-by-step explanation:
Divide by 3
1 : 4 : 3
between grid lines is 1 foot.
A. Is 30 feet of fencing enough to enclose the yard?
* C is twice as close to A as it is to B (there is more than one
answer)
Answer:
Angle at the center is two times the angle at circumferance
Elle and Scarlett were making a quilt. Elle completed 33 100 33100 of the quilt, and Scarlett completed 4 10 410 of the quilt. How much of the quilt have they completed together? A. 37 100 B. 73 100 C. 37 10 D. 73 10
The amount of quilt that they will both complete together= 37×10. That is option C.
Calculation of total quiltThe total amount of quilt made by Elle = 33×10
The total amount of quilt made by Scarlett= 41×10
To determine the total amount of quilt made by both individual, add the number of quilt achieved by each.
33×10 + 4×10 = 37×10
Therefore, the amount of quilt that they will both complete together= 37×10.
Learn more about summation here:
https://brainly.com/question/542712
If I have 53 shirts and have to get 100 shirts in 37 days, how many shirts do I have to get in less 37 day?
Answer:
if you have 53 shirts and have to get 100 shirts in 37 day's you will need to get 47 shirts
Find the surface area of the square pyramid shown below.
17 in
-15 in
16 in
What is the surface area of the pyramid in square inches?
0 736 square inches
o 800 square inches
0 1280 square inches
O 1451 square inches
Answer:
800
The surface area of the square pyramid is 800.
S.A.= area of base+area of four triangles.
Therefore the answer is 800.
what is 12 x q greater than 12 but less than 24 Enter a positive value for q that makes this statement true.
12 x q is greater than 12 but less than 24.Immersive Reader
(3 Points)
2 3/4
2 1/2
1 6/8
1 3/4
1 1/2
5/6
5Question
(1 Point) wich one is it and i need 2 answer's
Answer:
2 1/2 and 1 1/2
Step-by-step explanation:
Simplify.
(x2+4x)−(x2+6x−3)
10x−3
2x2+10x−3
−2x+3
−2x
Solution:
Note that:
Given expression: (x² + 4x) − (x² + 6x − 3)Remove the brackets
(x² + 4x) − (x² + 6x − 3)=> x² + 4x - x² - 6x + 3Combine like terms
x²(1 - 1) + x(4 - 6) + 3=> x²(0) + x(-2) + 3=> -2x + 320.4yd rounded to the nearest tenth use 3.14 as pi
Answer:
6
Step-by-step explanation:
Wrote a cpital letter the appears to have perpendicular line segments
Mr. Carnegie will buy pencils and pens for his students
for the school year.
• He can spend no more than $30 on pencils and pens.
• Pencils cost $0.15 each, and pens cost $0.75 each.
• He needs to buy at least 3 times as many pencils as
pens.
Which of the following systems of inequalities can be
used to determine the number of pencils that Mr.
Carnegie can buy?
O A. 0.15x + 0.75y 30 and y > 3x
OB. 0.15x +0.75y < 30 and y < 3x
OC. 0.15x +0.75y > 30 and 3y > x
D. 0.15x +0.75y < 30 and 3y
The system of inequalities that can be used to determine he number of pencils that Mr.Carnegie can buy is 0.15x +0.75y < 30 and y < 3x.
What are inequality sign and what do they mean?
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
What are the system of inequalities?The total amount spent on pens and pencils cannot exceed $30. Thus, the inequality sign to be used is <. Thus, the equation is: 0.15x +0.75y < 30 and 3x > y
To learn more about inequality, please check: https://brainly.com/question/5031619
What is the area of this trapezoid