Mister Exam
7,13+14,85*x+9,31*x^2+1,55*x^3<=6,754*x+57,64*x^2+33,08*x^3 inequation
The solution
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2 3 2 3 713 297*x 931*x 31*x 3377*x 1441*x 827*x --- + ----- + ------ + ----- <= ------ + ------- + ------ 100 20 100 20 500 25 25
$$\frac{31 x^{3}}{20} + \left(\frac{931 x^{2}}{100} + \left(\frac{297 x}{20} + \frac{713}{100}\right)\right) \leq \frac{827 x^{3}}{25} + \left(\frac{1441 x^{2}}{25} + \frac{3377 x}{500}\right)$$
31*x^3/20 + 931*x^2/100 + 297*x/20 + 713/100 <= 827*x^3/25 + 1441*x^2/25 + 3377*x/500
Solving inequality on a graph
Rapid solution
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/ / / 3 2 \ / 3 2 \ \ / / 3 2 \ \\ Or\And\x <= CRootOf\15765*x + 24165*x - 4048*x - 3565, 1/, CRootOf\15765*x + 24165*x - 4048*x - 3565, 0/ <= x/, And\CRootOf\15765*x + 24165*x - 4048*x - 3565, 2/ <= x, x < oo//
$$\left(x \leq \operatorname{CRootOf} {\left(15765 x^{3} + 24165 x^{2} - 4048 x - 3565, 1\right)} \wedge \operatorname{CRootOf} {\left(15765 x^{3} + 24165 x^{2} - 4048 x - 3565, 0\right)} \leq x\right) \vee \left(\operatorname{CRootOf} {\left(15765 x^{3} + 24165 x^{2} - 4048 x - 3565, 2\right)} \leq x \wedge x < \infty\right)$$
((x < oo)∧(CRootOf(15765*x^3 + 24165*x^2 - 4048*x - 3565, 2) <= x))∨((x <= CRootOf(15765*x^3 + 24165*x^2 - 4048*x - 3565, 1))∧(CRootOf(15765*x^3 + 24165*x^2 - 4048*x - 3565, 0) <= x))
Rapid solution 2
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/ 3 2 \ / 3 2 \ / 3 2 \ [CRootOf\15765*x + 24165*x - 4048*x - 3565, 0/, CRootOf\15765*x + 24165*x - 4048*x - 3565, 1/] U [CRootOf\15765*x + 24165*x - 4048*x - 3565, 2/, oo)
$$x\ in\ \left[\operatorname{CRootOf} {\left(15765 x^{3} + 24165 x^{2} - 4048 x - 3565, 0\right)}, \operatorname{CRootOf} {\left(15765 x^{3} + 24165 x^{2} - 4048 x - 3565, 1\right)}\right] \cup \left[\operatorname{CRootOf} {\left(15765 x^{3} + 24165 x^{2} - 4048 x - 3565, 2\right)}, \infty\right)$$
x in Union(Interval(CRootOf(15765*x^3 + 24165*x^2 - 4048*x - 3565, 0), CRootOf(15765*x^3 + 24165*x^2 - 4048*x - 3565, 1)), Interval(CRootOf(15765*x^3 + 24165*x^2 - 4048*x - 3565, 2), oo))