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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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tino4ka555 [31]

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DeSean is sorting his toy car collection. ⅔ of the cars are sports cars. ¼ of the remaining toys are pick up trucks. All of the
user100 [1]

Answer:

Fraction of fire trucks = \frac{1}{4}

Total number of toy cars = 16

Step-by-step explanation:

Fraction of sports car = \frac{2}{3}

Fraction of remaining cars =1-\frac{2}{3}=\frac{3-2}{3} =\frac{1}{3}

So,

Fraction of pick up cars = \frac{1}{4}(\frac{1}{3})=\frac{1}{12}

Therefore,

Fraction of fire trucks = \frac{1}{3}-\frac{1}{12}=\frac{4-1}{12}=\frac{3}{12}=\frac{1}{4}

That is Number of fire trucks = \frac{1}{4} ( Total number of toy cars )

Number of fire trucks = 4

Total number of toy cars = 4(4)=16

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2 years ago
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Answer:

Step-by-step explanation:

A. 16.6%

B. 16.6%

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