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

10344 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.


Find the equation of the straight line perpendicular to 3x+5y+6=0 that passes through (3,4)


The functions f and g are defined by f : x → 2x + ln 2, g : x → e^(2x). Find the composite function gf, sketch its graph and find its range.


The equation: x^3 - 12x + 6 has two turning points. Use calculus to find the positions and natures of these turning points.


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