Question

Help with question 3 inequalities using any of the 3 methods does not matter which one

Answer 1

The equation is given as,

`-3x^2\: +\: 24x\: -\: 3\: \le-3\text{ }`

Rearranging the constant terms on both the sides,

`\begin{gathered} -3x^2\: +\: 24x\: \le\text{ 0} \\ 3(-x^2\text{ + x ) }\le\text{ 0} \\ -x^2\text{ + x }\le\text{ 0} \end{gathered}`

Calculating the value of x ,

`\begin{gathered} -\text{ x (x - 8) }\le\text{ 0} \\ (-x(x-8))(-1)\ge\text{ ( -1)} \end{gathered}`

Simplifying,

`x(x-8)\text{ }\ge\text{ 0}`

Thus the intervals of x are,

`x\text{ }\le\text{ 0 or x }\ge\text{ 8}`