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

DD
Answered by Daisy D. Maths tutor

10376 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is 'grouping' and how does it work?


Using the product rule, differentiate y=(2x)(e^3x)


How do you integrate (x/(x+1)) dx without using substitution.


The line L1 has vector equation,  L1 = (  6, 1 ,-1  ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences