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Finger [1]
3 years ago
9

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics
2 answers:
rewona [7]3 years ago
6 0

Answer:

2nd option.

Step-by-step explanation:

3(8 - 4x) < 6(x - 5)

24 - 12x < 6x - 30

-12x - 6x < -30 - 24

-18x < -54

x > 3

Alexxandr [17]3 years ago
4 0

Answer:

2nd graph

Step-by-step explanation:

3(8 – 4x) < 6(x – 5)

Distribute

24 -12x < 6x -30

Add 12x to each side

24-12x+12x < 6x-30+12x

24 < 18x-30

Add 30 to each side

24+30 < 18x-30+30

54 <18x

Divide by 18

54/18 < 18x/18

3<x

Open circle at 3 and line going to the right

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Answer:  The required solution is

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Let us consider that

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Differentiating with respect to t, we get

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According to the given conditions, we have

y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

and

y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.

From equation (ii), we get

B=\dfrac{7}{3}.

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y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.

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