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

    17
    ReputationRep:
    Hi,

    I'm a bit confused about how to solve part b. I've done the "solve directly" method shown on the markscheme but I don't understand how they've gone from line 1 to line 2 (where has the modulus sign gone to?) I usually use the method where you square both sides to remove the modulus and it didn't work. I don't know whether it's supposed to work and I made a mistake or it shouldn't work for this question. Please could someone explain this to me.

    Thanks
    Attached Images
      
    Offline

    5
    ReputationRep:
    From the graph, they chose 2-x+1 instead of x-2+1 because it's the left branch of the function, which has a negative gradient (of -1). Given that the intersection point lies on the right branch of |x| (with a positive gradient), they replaced it with x.

    Squaring both sides would have worked. Expanding (|x-2|+1)^2, you should get (x-2)^2+2|x-2|+1, meaning you'll have to verify at the end if w\geq 0 in |x-2|=w.
    Offline

    14
    ReputationRep:
    Squaring only works if everything is in the modulus sign, so if you had mod(x)=mod(x-2+1), then squaring would work. Edit: didn't know squaring would work if the modulus sign was retained, interesting.

    You'd have to do it by considering both moduli to be positive, and then one to be negative. But, as there's only one intersection you only get one solution (1.5), which you get from the left branch, as MartyO says, that would have gone down below the y axis without the modulus
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 21, 2017
Poll
“Yanny” or “Laurel”
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

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