Question

solve the following inequality for x. express your answer in algebraic notation. if there is no solution, indicate
o solution.\ if all real numbers solve the inequality, indicate \all real numbers.\
5x² - 7x + 7 > 0
answer
you may type \or\ between inequalities, if necessary.
selecting one of the alternative options will replace the entered value(s) with the selected value. otherwise, the entered answer is used.
no solution
all real numbers

Explanation:

Step1: Calculate the discriminant

For the quadratic equation \(ax^{2}+bx + c = 0\) (\(a = 5\), \(b=-7\), \(c = 7\)), the discriminant \(\Delta=b^{2}-4ac\).

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Step2: Analyze the sign of the quadratic function

Since \(a = 5>0\) (the parabola \(y = 5x^{2}-7x + 7\) opens upwards) and \(\Delta=-91<0\) (the quadratic function \(y = 5x^{2}-7x + 7\) has no real roots).
The graph of the quadratic function \(y = 5x^{2}-7x + 7\) is always above the \(x\) - axis.

Answer:

All Real Numbers