What are the set of values for x that satisfy the below equation?

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What are the set of values for x that satisfy the below equation?

x² - 9x ≤ 36

1. Draw a graph.

y = x²- 9x and y = 36

2. Find the points of intersection by solving x² - 9x = 36

x² - 9x = 36

x²- 9x - 36 = 0

(x - 12)(x + 4) = 0

Therefore, the lines intersect at x = 12 and x = - 4

3. Either observe from your graph or plug in points either side of the points of intersection.

i) For x < -4

e.g. x = - 5. Sub. into LHS = (-5)²- 9(-5) = 70 > 36

ii) For -4 < x < 12

e.g. x = 0. Sub. into LHS = 0²- 9(0) = 0 < 36

iii) For x > 12

e.g. x = 20. Sub. into LHS = 20² - 9(20) = 400 - 180 = 220 > 36

Therefore, x² - 9x ≤ 36 when -4 ≤ x ≤ 12

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