Question #1eddb

1 Answer
Jul 2, 2017

(x + 68)/(x + 8) >= 5

We first multiply both sides by (x + 8)^2 as this is a positive quantity and won't change the inequality sign

i.e. (x + 68)(x + 8) >= 5(x + 8)^2

=> (x + 68)(x + 8) - 5(x + 8)^2 >= 0

=> (x + 8)[(x + 68) - 5(x + 8)] >= 0

so, (x + 8)(28 - 4x) >= 0

or, 4(x + 8)(7 - x) >= 0

This function is an inverted parabola which intersects the x-axis at -8 and 7

Hence, it is above the axis, or on it for -8 < x <=7

Note, we cannot have x = -8 as this value is excluded from the domain.

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