[tex] |7 + 8x| > 5[/tex]
I've tried solving this inequality multiple times and I just can't get it right. I don't know what I'm doing wrong. please help​

Answers

Answer 1

The absolute value is defined as

[tex]|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]

So for example, if x = 3, then |x| = |3| = 3, since 3 is positive. On the other hand, if x = -5, then |x| = |-5| = -(-5) = 5, since -5 is negative. The absolute value is always positive.

For the inequality |7 + 8x| > 5, you consider the two cases where the argument to the absolute value (the expression you find inside the bars) is either positive or negative.

• If 7 + 8x ≥ 0, then |7 + 8x| = 7 + 8x, so that

[tex]|7+8x|>5\implies 7+8x>5 \implies 8x>-2 \implies x>-\dfrac14[/tex]

• Otherwise, if 7 + 8x < 0, then |7 + 8x| = -(7 + 8x), so that

[tex]|7+8x|>5\implies-(7+8x)>5\implies7+8x<-5\implies8x<-12\implies x<-\dfrac32[/tex]

The solution to the inequality is the union of these two intervals.


Related Questions

Let sin(45°)=0.7071.Enter the angle measure (μ), in degrees for cos(μ)=−0.7071.
any value equivalent to 360n +
, wheren is an integer

Answers

Given :

Let sin(45°)=0.7071.

To Find :

The angle measure (μ), in degrees for cos(μ)=−0.7071 and value equivalent to 360n + , where n is an integer .

Solution :

We know , value of sin x and cos x is same at x = 45° .

Now , cos (-x) = cos(90°+x)

Therefore , μ in given question is :

μ =90°+45°

μ=135°

So , for angle of type 360°n + :

μ = 360°n + 135° .

Hence , this is the required solution .

vienna earns $53 per week working part time at a bookstore. She makes $1 more for each book that she sells. The amount, A (in dollars), that vienna earns in a week if she sells b books is given by the following function.
A(b)=53+b
how much does Vienna earn in a week if she sells 35 books?​

Answers

Answer:

$88 or $298

Step-by-step explanation:

take viennas $53 per week and add the extra $35 she makes for selling books and you get $88

or

take viennas $53 per week and add the extra $245 she makes for selling books and you get $298

the first is if she sells 35 books for the whole week, and i wrote the second one for if you mean she sells 35 books a day

(im not sure if this is right, but its the closest thing i can think of)

Answer:

88 or 298!

Step-by-step explanation:

take viennas $53 per week and add the extra $35 she makes for selling books and you get $88

or

take viennas $53 per week and add the extra $245 she makes for selling books and you get $298

the first is if she sells 35 books for the whole week, and i wrote the second one for if you mean she sells 35 books a day

(im not sure if this is right, but its the closest thing i can think of)

Evaluate the expression. ( 92 – 15 12) = 17 The value of the expression is​

Answers

Answer:

False

Step-by-step explanation:

Answer

false

Step by step

(92-1512)=17

3.
[tex] - \sqrt{49} [/tex]
find each square root​

Answers

Answer:

The negative square root of -49 is -7

-7

The root of 49 is 7 and the negative on the outside makes it -7

Which number line have a point that is equal to point p? Check all that apply

Answers

A and C is the answer

Answer: A and C

Step-by-step explanation:

The given box plots show the number of text messages Paul and Sally received each day on their cell phones. Select the true statement. * Captionless Image Paul's data has a larger overall spread than Sally's data. The median of Paul's data is equal to the median of Sally's data. The median of Paul's data is greater than the median of Sally's data. The interquartile range of Paul's data is less than the interquartile range of Sally's data.

Answers

Answer:

Its pauls data has a larger  overall spread than sally.

Step-by-step explanation:

I just took the test and I got a 100. :)

Please help! I will mark brainliest. Sketch the following graphs in order:

Answers

Answer:

Domain of f(x) = 2/7x - 2: (-∞, ∞)

Range of f(x) = 2/7x - 2: (-∞, ∞)

Domain of f(x) = |x + 3| - 1: (-∞, ∞)

Range of f(x) = |x + 3| - 1: [-1, ∞)

Domain of f(x) = -5x + 4: (-∞, ∞)

Range of f(x) = -5x + 4: (-∞, ∞)

Step-by-step explanation:

We can use a graphing calculator to find the graphs.

Domain is the set of all x-values that can be inputted into function x.

Range is the set of all y-values that can be outputted from function x.

You have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 100 dollars give or take 25. Write an inequality to describe the amount of money in your wallet.

Answers

Answer: 75 < x < 125.

Step-by-step explanation:

Let x be the amount of money in your wallet.  

The phrase "100 dollars give or take 25" means wallet can have money between (100-25) dollars and (100+25) dollars.

i.e. 100-25 < x < 100+25

⇒ 75 < x < 125.

That means the amount of money in your wallet lies between 75 dollars and 125 dollars.

Hence, the inequality to describe the amount of money in your wallet is 75 < x < 125.

find y if x = -3 whats the answer

Answers

A. y = 1/3 (-3) - 3 = - 6

B. y = 2(-3)^2 - 3(-3) - 2

= 2(9) - 3(-3) - 2

= 18 + 9 - 2

= 25

C. 2(-3) - 5y =4

- 6 - 4 = 5y

y = - 2

Answer:

A = -6

B = 25

C = 2

Step-by-step explanation:

-3*1/3 = -1, and -1-5=-6

2(-3)^2=2(9)=18   -3*-3=9    18+9=27    27-2=25

for the last rewrite the equation

2x-4=5y

-6-4=-10

-10=5y

y=-2

Write the improper fraction 33/10 as a mixed number

Answers

the answer is 3 3/10

hope this helps

Answer = 3 3/10

there’s 33 take away the ones that go to ten.

10 10 and 10 is 30. Therefore it’s 3 and 3/10

please help me i'm confused
(grade 7-8)

Answers

Best of my understanding, it would be 5+5, then 10+10, , 20+20 and so on, just add the numbers.

If a/\2+1/a/\2=11, then a+1/a=?

Answers

Answer:

[tex] \pm \sqrt{13} [/tex]

Step-by-step explanation:

[tex] \bigg(a + \frac{1}{a} \bigg)^{2} = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} \\ \\ \bigg(a + \frac{1}{a} \bigg)^{2} = 11 + 2 \\ \\ \bigg(a + \frac{1}{a} \bigg)^{2} = 13 \\ \\ \bigg(a + \frac{1}{a} \bigg) = \pm \sqrt{13} [/tex]

Frank has a sample of steel that weighs 80 grams. If the density of his sample of steel is 8 g/cm3, what is the sample’s volume?

Answers

Answer:

volume of the sample is 10 cm³

Step-by-step explanation:

volume = 80 g / 8 g/cm³

volume = 10 cm³

I hope this helps you :)

-KeairaDickson

Select the items from the following list that are included in financial literacy.

Answers

Answer:

applying for a credit card

paying taxes

opening a checking account

Step-by-step explanation:

Hope this will help yal'l

the difference of a number x and 5

Answers

Answer:

x-5

Step-by-step explanation:

"difference" means subtraction. since there isn't a specific number given then we can use x. "and" indicates where the symbols goes.

Evaluate the following function over the domain {0,1,2,3}. What is the range? g (x) = -2x^{2} + 2

Answers

Answer:

the range= {-16, -6, 0, 2}

Step-by-step explanation:

domain={0,1,2,3}

g(x)= -2x^{2} + 2

g(0)= -2(0)^{2} + 2 =2

g(1)= -2(1)^{2} + 2 =0

g(2)= -2(2)^{2} + 2= -6

g(3)= -2(3)^{2}+ 2= -16

the range = {-16, -6, 0, 2}

Evaluate the expression when g=3 and h=39.
h-5g

Answers

Answer:

29

Step-by-step explanation:

g=3 h=39

h-5g

Substitute the values in for the variables :

39-5(3)

Order of operations: multiply first

39-15

=24

Hope this helps :)

Write 3.24 x 10-4 in standard notation.

Answers

3.24 x 10-4 in standard notation is 0.000324

Point B is on line segment AC. Given AB = 2x + 10, BC = x, and AC = 5x,
determine the numerical length of AC.

Answers

Answer:

AC = 25

Step-by-step explanation:

Since B is on the segment AC, then

AC = AB + BC, substitute values

5x = 2x +10 + x , that is

5x = 3x + 10 ( subtract 3x from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Thus

AC = 5x = 5(5) = 25

A triangle has side length of

Answers

3.8q + 21.2 + 8.3r

The perimeter is all sides added together, therefore our equation looks like this:

[tex](1.7q + 9.3) + (2.1q + 6.7) + (8.3r + 5.2)[/tex]

However, we can get rid of the parentheses and add like terms together.

[tex]1.7q + 9.3+ 2.1q + 6.7+ 8.3r + 5.2[/tex]

[tex]1.7q + 2.1q + 9.3 + 6.7+ 5.2 + 8.3r [/tex]

[tex] 3.8q + 21.2 + 8.3r [/tex]

what is 18 less than the quotient of a number and 3 as an expression

Answers

Answer:

n/3 - 18

Step-by-step explanation:

"quotient of a number and 3" is n/3, and so

"18 less than the quotient of a number and 3" as an expression is:

   n/3 - 18

An up-and-coming artist has 85 followers on Twitter and this number doubles every week. In what week will the artist first reach 1,000 followers? Use at least two different methods to come up with your answer.

Answers

Answer:

5.8 , which approximately is 6 weeks.

Step-by-step explanation:

the first method is the short one since u just have to double the 85 then divide to 1000.

1000 ÷ ( 85 × 2)

1000 ÷ 170 = 5.882,,,,,. round off to whole number to get 6.

the second method is the addition method.

we start by 85 then keep doubling 85 for every week........inshort.......we add 170 to each weeks number to get the number of followers for the following week.

85 ⇒ 170 ⇒ 340 ⇒ 510 ⇒ 680 ⇒ 850 ⇒ 1020.

     1st      2nd      3rd     4th      5th         6th     week.

u notice that we add (85×2), 170, to get the following week's number of followers..

in 5 weeks..... the number of followers is yet to get to 1000.

when u divide, u get 5.8.....,and it is not logic to say 5.8823....weeks

since she reaches 1000 followers in the 6th week.......though there is an addition,,,, it is the most appropriate answer.

It will take [tex]6[/tex] week to reach [tex]1000[/tex] followers.

First, we are using two step to find the answers.

  Division   Addition

Division:

   By given, A artist has [tex]85[/tex] followers.

Every week  the no. of. followers is doubled .

Now, find how many week the artist reach [tex]1000[/tex] followers.

Since week followers is doubled,

So ,[tex]85*2[/tex]

Thus,

 [tex]1000\div(85*2)\\\\=1000\div170\\\\=5.883[/tex]

Which is not possible .

Then, it take [tex]6[/tex]  week to reach the  [tex]1000[/tex] followers.

Addition:

    By given, A artist has [tex]85[/tex] followers.

Every week  the no. of. followers is doubled .

To find how many week the artist reach [tex]1000[/tex] followers.

Now, the first week has [tex]85[/tex] followers.

[tex]85[/tex] followers doubled.

[tex]85+85=170[/tex] followers doubled in every week .

Then,

Second week has   [tex]85+85=170[/tex] followers.Third week has    [tex]170+170=340[/tex] followers.Fourth week has  [tex]340+170=680[/tex] followers.Fifth week has      [tex]680+170= 850[/tex] followers.Sixth week has     [tex]850+170= 1020[/tex] followers.

Hence, the artist reach [tex]1000[/tex] followers in mid week of [tex]5[/tex] to [tex]6[/tex] week .

so, it approximately take  [tex]5.88[/tex] week to reach [tex]1000[/tex] followers but which is impossible to take decimal in week .

Thus, the artist take [tex]6[/tex] week to reach the [tex]1000[/tex] followers.

For more information:

https://brainly.com/question/17367033

What is the distance from M(-1, 6) to N(11, 1)?

Please show all work and not just the answers.

Answers

Distance = sqrt(x1-x2^2 + y1-y2^2)

Distance = sqrt((-1-11)^2 +(6-1)^2)

Distance = sqrt(12^2 + 5^2)

Distance = sqrt(144 + 25)

Distance = sqrt(169)

Distance = 13

solve this please
[tex]5x - 2(4x + 11) = 14[/tex]

Answers

Answer:

Step-by-step explanation:

5x - 8x - 22 = 14

-3x - 22 = 14

-3x = 36

x = -12

Answer:

x = -12

Step-by-step explanation:

5x - 2(4x+11) = 14

5x - 2*4x -2*11 = 14

5x - 8x - 22 = 14

-3x = 14 + 22

-3x = 36

x = 36/-3

x = -12

Check:

5*-12 -2(4*-12 + 11) = 14

-60 -2(-48+11) = 14

-60 -2(-37) = 14

-60 + 74 = 14

What is the rule for the transformation from the smaller polygon to the larger polygon?

Answers

i think the answer is B

Find the x- and y-intercepts of the graph of the linear equation. y=-x+4

Answers

Answer:

Step-by-step explanation:

x-int

-x + 4 = 0

x = -4

(-4, 0)

y-int

y = 0 + 4

y= 4

(0, 4)

Is 8/5
an irrational number?

Answers

No, it’s not. It’s a rational number

AB lies on a number line. The coordinate of point A is -6. Given that AB=20, what are two possible coordinates for point B?

Answers

Answer:

-26 or 14

Step-by-step explanation:

Given that

Coordinate of point A is -6.

Length of AB = 20

To find:

Coordinates for the point B = ?

Solution:

We are given that:

AB = 20

In other words, we can use modulus function to define the distance between A and B:

|Coordinates of B - Coordinates of A| = 20

Let the coordinates of B = [tex]x[/tex]

Kindly refer to the attached image for the given situation.

Point B might be either on the left or on the right side of A.

That means:

[tex]|x-(-6)| = 20\\\Rightarrow |x+6|=20[/tex]

Now, let us have a look at the modulus function:

[tex]|y|=\left \{ {-{y}\ if\ y<0 \atop {y}\ if\ y>0} \right.[/tex]

So,

[tex]|x+6|=\left \{ {-{(x+6)}\ if\ (x+6)<0 \atop {(x+6)}\ if\ (x+6)>0} \right.[/tex]

[tex](x+6 ) =20\\\Rightarrow x =14[/tex]

[tex]-(x+6 ) =20\\\Rightarrow x =-26[/tex]

Therefore, the answer is:

-26 or 14

How do you write 8409.08 in words?

Answers

Answer:

eight thousand four hundred nine and eight hundredths

Step-by-step explanation:

Answer:

The answer is, Eight-thousand four-hundred nine and eight thousandth

Step-by-step explanation: All you have to do is say it enough. Please have a nice day.

k to the power of 8 times k

Answers

Steps to solve:

k^8 * k

~Since we are multiply k to itself, we just add one to the exponent of 8.

k^8+1

k^9

Best of Luck!

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