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natita [175]
3 years ago
10

What is the solution set of the compound inequality x+1<-2x+11<3x+5

Mathematics
1 answer:
VikaD [51]3 years ago
6 0

Answer:

6/5 < x < 10/3 is the desired solution.

Step-by-step explanation:

Here, the given compound inequality is :

x + 1 < -2 x + 11 < 3 x + 5

Now, consider the first two term of the inequality, we get:

x + 1 < -2 x + 11

Subtracting 1 from both sides, we get:

x + 1  - 1 < -2 x + 11  - 1

or, x < -2x + 10

or, x + 2x < 10

or, 3 x < 10

or, x <  10/3

Similarly, considering the last two terms of the given inequality, we get:

-2 x + 11 < 3 x + 5

Subtracting 11 from both sides, we get:

-2 x + 11  - 11 < 3 x + 5 - 11

or, - 2 x < 3 x-6

or, 6 < 5 x

or, x > 6/5

Hence, combining two solutions, we get:    6/5 < x < 10/3

So, the desired value of x should be more than (6/5) but less than (10/3)

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1) you can expand the brackets, simplify, set the equation = 0 and then do a double bracket factorisation.

(x - 4)^{2}   - 28 = 8 \\ x - 8x + 16 - 28 = 8 \\ x - 8x - 12 = 8 \\ x - 8x - 20 = 0 \\ (x - 10)(x  + 2) = 0 \\  x = 10 \\ x =  - 2

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