The solution to the given inequality is; x ≥ -9/4 or x ≥ 1
How to solve Inequality problems?
We want to solve the inequality;
(4x² + 5x - 9)/(x² - x - 6) ≥ 0
Let us factorize both numerator and denominator to get;
4x² + 5x - 9 = (4x + 9)(x - 1)
Similarly, x² - x - 6 when factorized gives;
x² - x - 6 = (x + 2)(x - 3)
Thus, we now have;
[(4x + 9)(x - 1)]/[(x + 2)(x - 3)] ≥ 0
Multiply both sides by [(x + 2)(x - 3)] to get;
(4x + 9)(x - 1) ≥ 0
Thus;
(4x + 9) ≥ 0 or (x - 1) ≥ 0
Thus;
x ≥ -9/4 or x ≥ 1
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