Question

find the common solution of following inequality (x-7)(x-15)<0, (x-2)(x-8)(x-12)≥0​

Answer 1

Step-by-step explanation:

x - 7)(x - 15) ≤ 0 , (x - 2)(x -8)(x - 12) ≥ 0

find solution for (x - 7)(x - 15) < 0

first replace inequality sign by equal

e.g., (x - 7)(x - 15) = 0 ,

x = 7, 15

now, put 7 and 15 in number line .

And apply the condition of inequality ,

we get 7 < x < 15

Similarly find the solutions of (x - 2)(x - 8)(x - 12) ≥ 0

replace inequality by equal

And we get x = 2, 8, 12 now put it in number line.

apply condition we get , 2 ≤ x ≤ 8 or, x ≥ 12

Now, take common solution of it using all numbers { e.g., 2, 7, 8, 12, 15} in number line .

see attachment , we get the solution x ∈(7, 8] ∪ [12, 15)

Answer 2

Answer:

Hey mates

Here is your answer

x - 7)(x - 15) ≤ 0 , (x - 2)(x -8)(x - 12) ≥ 0

find solution for (x - 7)(x - 15) < 0

first replace inequality sign by equal

e.g., (x - 7)(x - 15) = 0 ,

x = 7, 15

now, put 7 and 15 in number line .

And apply the condition of inequality ,

we get 7 < x < 15

Similarly find the solutions of (x - 2)(x - 8)(x - 12) ≥ 0

replace inequality by equal

And we get x = 2, 8, 12 now put it in number line.

apply condition we get , 2 ≤ x ≤ 8 or, x ≥ 12

Now, take common solution of it using all numbers { e.g., 2, 7, 8, 12, 15} in number line .

see attachment , we get the solution x ∈(7, 8] ∪ [12, 15).

I hope this answer help you

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