9514 1404 393
Answer:
0.25 < x < 2
Step-by-step explanation:
The quadratic can be factored as ...
4x^2 -9x +2 < 0
(4x -1)(x -2) < 0
The factors are zero for x = 1/4 and x = 2. The product of the factors will be negative, satisfying the inequality, for values of x that make one factor positive and the other one negative. Those values of x are between x=1/4 and x=2.
The solution is 1/4 < x < 2.
The graph on the number line has open circles at x=1/4 and x=2, and is shaded between those values.
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Additional comment
The circles on the graph are open because those x-values are not part of the solution set.
