Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter

    I just want to quickly check something.

    If you have an inequality such as:
    x2 > 16

    Root 16 is + or - 4, right?

    Therefore, I, at first thought eh answer would be:
    x > 4
    x > -4

    and hence the only real solution is:
    x > -4

    But, the mark scheme said that the answer would be #
    x > 4 and x < -4

    Does this mean that for the negative one, we have to switch the inequality over, just like we do if me multiple the expression by -1?

    In response to the mark scheme, if x(squared) has to be bigger than 16 then the numbers after 4 (5,6,7,8....) will satisfy this inequality. This is why 'x' must be bigger than 4 and less than -4 so the numbers beyond these limits can satisfy the inequality. So if x=-1 was put it, it would not satisfy the equation and in order for it to do so the sign > would have to be switched <.

    re-arrange the inequality as: x^{2}-4^{2}&gt;0

    another way to look at this is - it`s saying: where is the y value positive?

    think about the plot of y=x^{2}-16=(x+4)(x-4)

    this is symmetrical about the y-axis, and has a minimum y value of -16, and roots at +4 and -4. So it is concave up from y=-16, and so negative in the range -4&lt;x&lt;4 AND POSITIVE EVERWHERE ELSE. (x>4, x<-4)
    Attached Images

    (X^2) > 16
    (x^2) - 16 > 0

    draw a graph of x squared -16, it will cross the x-axis at 4 and -4. now you want all the places where the graph is bigger than zero, so basically all the places above the x-axis. so the line is above the x-axis when x is less than -4, and when x is greater than 4, but not anywhere between -4 and 4

    hence -4>x and 4<x

    can you see that on the graph, let me know
How are you feeling about your exams?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.