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
Scrat [10]
3 years ago
14

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5

< 7 or 4x + 10 > 6 is .
Mathematics
1 answer:
lisov135 [29]3 years ago
6 0

Solution for Part 1:

2x − 5 < 7 and 4x + 10 > 6 is called a compound inequality. To find the range we need to solve each of the inequality and range would be the values of x which will make both the inequality TRUE.

Solving inequality 2x - 5 < 7:

2x - 5 < 7 {adding 5 on both sides}

2x - 5 + 5 < 7 + 5 {Combining like terms in either side of inequality}

2x < 12 {Dividing 2 on both sides}

2x/2 < 12/2 {Simplifying fraction in either side of inequality}

x < 6

Solving inequality 4x + 10 > 6:

4x + 10 > 6 {Subtracting 10 on both sides of inequality}

4x + 10 - 10 > 6 -10 {Combining like terms on either side}

4x > -4 {Dividing by 4 on both sides}

4x/4 > -4/4 {Simplifying each fraction}

x > - 1

Range of 2x − 5 < 7 and 4x + 10 > 6 will be all the x value which satisfy both the inequality x < 6 and x > -1.

Conclusion Part 1:

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is can be given by interval notation (-1, 6)

Solution for part 2:

2x − 5 < 7 or 4x + 10 > 6 is called a compound inequality. To find the range we need to solve each of the inequality and range would be the values of x which The solution is same as part 1, with a small difference.

Range of 2x − 5 < 7 or 4x + 10 > 6 will be all the x value which satisfy any one of the inequality x < 6 or x > -1.

Conclusion Part 2:

The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is can be given by interval notation (-∞, ∞)

Note:

(i) When two inequalities are joined by the word and, the solution of the compound inequality occurs when both inequalities are true at the same time. It is the overlap, or intersection, of the solutions for each inequality.

(ii) When the two inequalities are joined by the word or, the solution of the compound inequality occurs when either of the inequalities is true. The solution is the combination, or union, of the two individual solutions.

You might be interested in
Norma bought a plastic bag that contains 100 ballons the lable says that there are 20 each of blue,yellow, red, ,green and orang
Volgvan

Answer:

It is 120

Step-by-step explanation:

7 0
3 years ago
PLEASE Answer
Burka [1]
A......



A................


A..... A
5 0
3 years ago
Helpppp please :) dtchdtgddxxdcrvtgh
sergey [27]
6 cans of paint for a total of 90 dollars spent
I multiplied 120 by .20 to get 24 and subtracted it from 120 to get the amount that still has to be painted which is 96.
96 divided by 16 is 6 which is the number of cans of paint needed to paint the rest. Then just multiply by the cost (15$) and the answer is 90$
3 0
3 years ago
Read 2 more answers
A rectangle has an area of x^3 + 5x^2 + 5x – 2 square meters and a width of x + 2 meters. Find its length.
musickatia [10]

Answer: x^2 + 3x - 1.

Step-by-step explanation: We need to divide x^3 + 5x^2 +5x-2 by x+2. This is dividing polynomials. Divide each number by x and multiply the quotient by 2 and subtract the answer.

5 0
3 years ago
Solve the inequality 3 -2a &gt; 7
Paul [167]
3 - 2a > 7
We need to solve for a

First, let's subtract 3 on both sides to have the variables on a side and the numbers on another side:
3 - 2a > 7
3 - 2a - 3 > 7 - 3
- 2a > 4

Let's divide both sides by -2 to have a on side and its value on the other side:
-2a > 4
(-2a)/(-2) > (4/-2)
a < -2 (In a case of an inequality, we change the sign when we divide by a negative number to its opposite).

So 3 - 2a > 7 when a < -2 (answer c)

Hope this helps! :D

3 0
3 years ago
Read 2 more answers
Other questions:
  • A survey concluded that 60% of cars going through the Lomonosov street encounters traffic jam. After installing a new traffic li
    13·2 answers
  • SAT Scores Group 1 1520 1630 1480 1580 1400 1300 1700 1610 1580 1520 SAT Scores Group 2 1510 1480 2100 1800 1300 1250 1400 1430
    11·2 answers
  • Yesterday your bus ride took 10 minutes. Today your bus ride took 12 minutes. What is the percent of change?
    8·2 answers
  • what is the first to last in this question 1,450 1,776 1,670 1,483 which one is the smallest and which is the biggest
    15·2 answers
  • What is the distance between -2 and 5
    9·1 answer
  • Which formula gives the zeros of y = sin(x)?
    5·1 answer
  • What is the measure of ABC?<br><br> A 44°<br> B 88°<br> C 176°<br> D 92°
    14·1 answer
  • Write an equation for :<br><br> Three times a number decreased by five is equal to twenty five.
    8·1 answer
  • Can you please help me with this very hard math problem?
    15·2 answers
  • Which statement about determining the quotient 1/8 ÷ 2 is true?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!