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Solve using internet notation

Solve using internet notation-example-1

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It is to be noted that where the above is given, the correct answer is

x < (-9/2) + (-1/2) √(69)


(x-5)/(x² + 9x + 3) ≤0

Let's find the critical points of the inequality.

(x-5)/(x² + 9x + 3) = 0

x - 5 = 0 (Multiply both sides by x² + 9x + 3)

x - 5 + 5 = 0 +5 (Add 5 to both sides)

x = 5

Check possible critical points

x = 5 (Works in Original Equation)

Critical Points:

x = 5 (Make both sides equal)
x = -9/2 + 1/2√(69) or x = -9/2 + -1/2 √(69) (Makes left denominator equal to 0)

Check intervals in between critical points. Test values in the intervals to see if they work.

x < -9/2 + -1/2√(69) (works in original inequality)

-9/2 + -1/2√(69) < x < -9/2 + 1/2√(69) (doesn't work in original inequality)

-9/2 + 1/2√(69) < x ≤ 5 (Works in original inequality)

x ≥ 5 (Doesn't work in original inequality)

User Quamber Ali
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