# Algebra

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Solve x^2 -3x is greater than or equal to 10

Would the solutions be x=5 and x= -2?

• Algebra -

no, you forgot about the inequality condition.

(x-5)(x+2) ≤ 0

here is a neat way to finish it
draw a line and mark the "critical values" of -2 and +5
this splits the line into 3 segments
1. x < -2
2. x between -2 and 5
3. x > 5

pick any x you want in each of the segments to test . You don't actually have to find the value just the +/- situation

1. let x = -10 , so (-)(-) > 0 , NO
2. let x = 0 , so (-)(+) < 0 YEs
3. let x = 10, then (+)(+) > 0, NO

so every value of x between -2 and 5 inclusive will work..
-2 ≤ x ≤ 5 , x any real number

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