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

Answered by Daisy D. Maths tutor

8887 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

differentiate the following to find the equation for the gradient of the curve in terms of x and y: 3x^3 + 4x^2 + 5xy + 7y = 0


How to do Integration by Parts?


Differentiate (x^2)cos(3x) with respect to x


OCR M2 A level maths June 2015 question 8


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy