Question

!!!!! 60 POINTS !!!!!!!

I know the answer is −2.5  y  6, but how would you go about solving this? Please provide an explanation + formulae/rules if needed. Thank you!

Answer 1

Answer :

• -2.5 ≤ y ≤ 6 .

Solution :

factorise using the double split method

• 2y^2 - 7y - 30 ≤ 0
• 2y^2 + 5y - 12y - 30 ≤ 0
• y(2y + 5) - 6(2y + 5) ≤ 0
• ( y - 6)(2y + 5) ≤ 0
• y ≤ 6 ; -5/2 ≤ y

thus, our inequality would be

• -2.5 ≤ y ≤ 6 .

Answer 2

Answer:

Step-by-step explanation:

The inequality expressed here is quadratic due to 2 being the highest power, so we have to find y.

We can do this by factorizing $2y^{2}$-7y-30 into two brackets: (2y+ )(y+ ) so that $2y^{2}$ can be made.

Typically in the equation $ax^{2}$+bx+c, the two constants in the brackets multiply to make a x c and add up to make b. So, these two numbers have to be multiplied to -60 and add up to -7.

These two numbers are 5 and -12.

As -12 is divisible by 2, it should be put on the bracket containing (y+ ). The latter bracket should be (y-6) as its factor 2 is transferred to (2y+ ).

Therefore the other bracket should be (2y+5).

Now, setting each factor to 0, we have 2y+5$\leq$0 and y-6≤0. Make one side a multiple of y: 2y≤-5 and y≤6. For the first equation divide both sides by  2 so you get y≤-2.5.

Hope that helps!