1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sdas [7]
3 years ago
13

Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.

Mathematics
1 answer:
laila [671]3 years ago
6 0

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
  • if |a|< b then a<b or a>-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

You might be interested in
A health study tracked a group of person for five years. At the beginning of the study, 20% were classified as heavy smokers, 30
Aleks04 [339]

Answer: 0.421

Step-by-step explanation:

Heavy smoker = 20%

Light smoker = 30%

Non smokers = 50%

We can assume that the probability that a non-smoker is going to die in the next 5 years be y.

Since light smokers were twice as likely as nonsmokers to die during the five-year study, the probability will be:

= 2 × y = 2y

Probability for the Heavy smokers will be:= 2 × 2y = 4y

The expected number of people that will die for each in the next 5 years will be:

Non smoker:

= 50% × y

= 0.5 × y

= 0.5y

Light smoker:

= 30% × 2y

= 0.3 × 2y.

= 0.6y

Heavy smoker:

= 20% × 4y.

= 0.2 × 4y

= 0.8y

Total = 0.5y + 0.6y + 0.8y = 1.9y

The probability that the participant was a heavy smoker will be:

= 0.8y/1.9y

= 0.421

3 0
3 years ago
Two equations are given below:
goldenfox [79]
Since the second equation gives a value for a, we can substitute it into the other equation to find a value for B.

Let's substitute b-2 into the first equation wherever there is an a.

a - 3b = 4
(b-2) - 3b = 4
b - 2 - 3b = 4
-2 - 2b = 4
-2b = 6
b = -3

Now let's find a by substituting -3 into either of the equations to find the value of a.

a = b - 2
a = -3 - 2
a = -5

So your solution set  is (-5, -3)
4 0
3 years ago
Fill in the blank
Andrej [43]

Answer:

    dont click that link report it

Step-by-step explanation:

8 0
2 years ago
Find the scale factor using the distance formula.
Julli [10]
1/2 because everything lose half its value points wise.
3 0
2 years ago
NEED HELPPPP PLEASEEE!!! NUMBER 5 ONLY
Reika [66]

Answer:

Let x equal the ice thickness. An equality that represents a safe ice thickness for walkability is:

x ≥ 4 inches

(Plus the graph)

Step-by-step explanation:

Defining a variable just means you let any letter or symbol take the place of something. But you have to specifically say what is what in order for it to be clear.

So I defined "x" as the variable to represent the ice's thickness. And since we want an inequality for all the safe thicknesses, we could say that "x" must be greater than or equal to 4 inches thick in order to safely walk on it.

Lastly, you'd graph it with a solid point on 4 with the arrow going to the right.

7 0
3 years ago
Other questions:
  • What is -40 divided by (-5)
    8·1 answer
  • HELP!! 15 Points!!
    5·1 answer
  • I would hate to ask another question but Avery had $25.63 in her wallet. If she bought lunch with 7 1/4 dollars from her wallet,
    12·2 answers
  • A class is going on a field trip to see a movie. Each ticket is $6.00. The number of students, n, who will receive a $6.00 ticke
    12·1 answer
  • suppose a customer makes a purchase that costs $7.19 and pays with a ten dollar bill describe two ways you could calculate how m
    8·1 answer
  • When Justin purchased a new kayak, he paid a 6% sales tax. The amount of sales tax he paid was $84. What was the total cost of t
    13·1 answer
  • Multiply or divide as indicated <br> b^3 x b^-3
    13·1 answer
  • Round 94.62 to the nearest square inch
    12·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3-6y%7D%20%2B%20%5Cfrac%7B1%7D%7By%7D%20%3D%20%5Cfrac%7B1%7D%7B6%5C%5C%7D" id
    13·1 answer
  • Use a calculator to find decimal estimates to two decimal places (hundredths) for the following irrational number: √19​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!