Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

How to express each of the following pairs of
simultaneous inequalities in the form
a * x * b where a and b are numbers and #
may be < or <,
(a) x > 3, 2x - 3 < 15
(b) 25 > 1 - 6x, 1 > 3x + 7
(c) 2x - 7<3< 27 + 4x
(d) 3x + 8 <0 < 21 + 4x
(e) 5x - 36 < -1 < 2x – 1​

Sagot :

abidemiokin

Answer:

a) 3<x<8

b) -4<x<-2

c) -6<x<5

d) -21/4 < x-8/3

e) 0<x<7

Step-by-step explanation:

Given the following inequalities

a)  x > 3, 2x - 3 < 15

Solve 2x - 3 < 15

2x < 15+3

2x<18

x<18/2

x<8

Combine x>3 and x<8

If x>3, then 3<x

On combining, we have:

3<x<8

b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7

25 > 1 - 6x

25-1>-6x

24>-6x

Divide through by -6:

24/-6 > -6x/-6

-4 <x

For the inequality 1 > 3x + 7

1-7>3x

-6>3x

-6/3 > 3x/3

-2 > x

x < -2

Combining both results i.e -4 <x and x < -2, we will have:

-4<x<-2

c) For the inequalities 2x - 7<3< 27 + 4x

On splitting:

2x - 7<3 and 3< 27 + 4x

2x < 3+7

2x<10

x<5

Also for 3< 27 + 4x

3-27<4x

-24<4x

-24/4 < 4x/4

-6<x

Combining both solutions i.e x<5 and -6<x will give;

-6<x<5

d) For the inequalities 3x + 8 <0 < 21 + 4x

3x + 8 <0

3x < -8

x < -8/3

Also for 0 < 21 + 4x

0-21<4x

-21<4x

-21/4 < 4x/4

-21/4 < x

Combining -21/4 < x and x < -8/3 will give;

-21/4 < x-8/3

e) For the inequalities 5x - 36 < -1 < 2x – 1​

Split:

5x - 36 < -1

5x < -1+36

5x<35

5x/5 < 35/5

x < 7

For the expression -1 < 2x – 1​

-1+1 < 2x

0 < 2x

0<x

Combining both inequalities 0<x and x < 7 will give:

0<x<7

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.