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

Help with question 3 inequalities using any of the 3 methods does not matter which-example-1
User Ihightower
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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}

User Rezo Megrelidze
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