Question

Question #1eddb

Answer 1

`(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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