Question

Solve the inequality -2x² + 12x > 18.A.x > 3OB.x <3C. no solutionsOD.x>-3

Answer 1

Explanation

We are given the following inequality:

`-2x^2+12x>18`

We are required to solve the given inequality.

This is achieved thus:

`\begin{gathered} -2x^2+12x>18 \\ \text{ Divide through by 2} \\ -x^2+6x>9 \\ \text{ Rewrite in standard form} \\ -x^2+6x-9>0 \\ -(x^2-6x+9)>0 \\ \text{ Multiply both sides by -1} \\ x^2-6x+9<0 \\ \text{ Using grouping method} \\ x^2-3x-3x+9<0 \\ (x^2-3x)(-3x+9)<0 \\ x(x-3)-3(x-3)<0 \\ (x-3)(x-3)<0 \\ (x-3)^2<0 \\ \text{ Hence, there is no solution} \end{gathered}`

Hence, the answer is:

`No\text{ }solutions`