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3 votes
12 < y(8 - y)

how do i solve this please give me all the steps :)

User Minhaz
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1 Answer

2 votes

Answer:

2 < y < 6

Explanation:

Expand the brackets, multiplying by y

12 < 8y - y^2

Rearrange

0 < -y^2 + 8y - 12

Divide by -1. When dividing by a negative number, you must flip the inequality sign

0 > y^2 - 8y + 12

Factorise

0 > (y - 6)(y - 2)

The two solutions are y = 6, 2

Check using a value inbetween 2 and 6 to see if the inequality holds true. For example 3 is between 2 and 6

0 > (3 - 6)(3 - 2)

0 > -3(1)

0 > -3

As this holds true, this means that y lies between 2 and 6

Therefore, the answer is 2 < y < 6

(If the inequality did not hold true, then y would lie above 6 and below 2. y < 2 and y > 6. Not relevant for this example)

User Deltanovember
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