gbisnik wrote:

(10-w)(9-w) < 9 ... implies w > 6 ...how?

w(w-1) > 45 ..implies w>7...how?

I'm not able to derive the implication mathematically..Please help.

This is an inequation and not an equation (equation means equality between two algebraic expressions).

An inequation, usually has infinitely many solutions.

You can rewrite

(10-w)(9-w)<9 as

w^2-19w+81<0.

The equation

y=w^2-19w+81 is the equation of an upward parabola, which intersects the horizontal axis at the roots of the equation

y=0. Sketch the graph of the parabola after you find/estimate the roots, then read from the graph the values for which the inequality holds. For an upward parabola, the expression is negative for the values of the variable between the two roots and positive for values less than the smallest root or greater than the largest root.

In this case, the roots are pretty ugly (

\frac{19\pm\sqrt{37}}{2}), approximately 12.5 and 6.45, so the given expression is negative for

w between the previous two values. If

w is an integer, then it cannot be greater than 6.

Proceed similarly with the second inequality.

Good luck!

_________________

PhD in Applied Mathematics

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