Maths help!!!! (1 Viewer)

[JasonNg]

Hey guys,

Can you guys please show me how to do this problem? Been stuck on it for over an hour.

Solve |t + 2| + |3t - 1| < 5

Can you guys show me how to solve it graphically and/or algebraically. Thanks a lot! + rep btw

 

[Carrotsticks]

The general method is to take 'cases'.

I will list all the cases and you can easily work out the inequalities resulting from all the cases:

#1: Both are positive:

t + 2 + 3t - 1 < 5 =====> t < 1

#2: Left one positive, right one negative:

t + 2 + -(3t - 1) < 5 =====> t > -1

#3: Left one negative, right one positive:

-(t + 2) + 3t - 1 < 5 =====> t < 4

#4: Both are negative:

-(t + 2) + -(3t - 1) < 5 =====> t > -1.5

So we pick the domain that satisfies ALL of the conditions, which is -1 < t < 1.

 

[JasonNg]

OMG! I did exactly the same thing but messed up in my working out. Thanks so much Carrotsticks. + rep!!!

 

[JasonNg]

Dammit! "You must spread some reputation around before giving to Carrotsticks again" Farr... I'll definitely remember to rep you when i can

 

[SpiralFlex]

Consider the cases:



This can hold two "separate equations if you like"




Now let us consider



Hence the possible cases,



This also covers the solution of

So we take the branches.






Now, consider








Now finally consider,







Hence graphing each one separately we get,



(Note: This is the graph of |t+2|+|3t-1|-5, we focus on the part BELOW)



Alterative method:

 

[SpiralFlex]

Getting slower these days....

 

[nightweaver066]

Getting slower these days....

You should be preparing for your exams.

 

[Drongoski]

Getting slower these days....

Age catching up with you. I should know.

 

[Carrotsticks]

Age catching up with you. I should know.

2000th post.

 

[JasonNg]

Wow, your way is very confusing Spiral O.O