# Question

• Aug 2nd 2013, 06:51 PM
Matt512
Question
(i)Sketch on the same diagram the graphs of y = |2x+3| and y = 1-x
(ii)Find the values of x for which x + |2x+3|= 1
• Aug 2nd 2013, 06:58 PM
Prove It
Re: Question
Are you using the /symbol to represent absolute values? If so, you should really use |
• Aug 2nd 2013, 07:08 PM
Matt512
Re: Question
I equated the two equation and got x^3 - 5x + 2= 0
I find the f(2) = 0 which is (x-2) is a factor of x^3 - 5x + 2
• Aug 2nd 2013, 07:20 PM
johng
Re: Question
Hi matt512,
The attachment shows the graph and indicates how you can solve the equation.

Attachment 28939
• Aug 9th 2013, 09:49 AM
HallsofIvy
Re: Question
Quote:

Originally Posted by Matt512
I equated the two equation and got x^3 - 5x + 2= 0
I find the f(2) = 0 which is (x-2) is a factor of x^3 - 5x + 2

I have no idea what you are saying here. HOW did you "equate" the two equations? One is linear and the other an absolute value. I can't imagine how you could get a cubic from that. And then you say "I find the f(2)". What??? There is no "f" anywhere in the problem!

From the definition of "absolute value", |2x+ 3| is either 2x+ 3 or -(2x+ 3) depending upon whether 2x+3 is positive or negative. If $2x+3\ge 0$, then |2x+3|= 2x+ 3. Setting that equal to 1- x gives 2x+ 3= 1- x. Adding x- 3 to both sides, 3x= -2 so x= -2/3. Checking, 2(-2/3)+ 3=-4/3+ 9/3= 5/3 which is, indeed positive so that is a valid solution. If $2x+ 3\le 0$, then |2x- 3|= -(2x- 3)= 3- 2x. Setting that equal to 1- x give 3- 2x= 1- x. Adding 2x- 1 to each side 4= x. 2(4)+ 3= 11 which is positive so that is a valid solution.

|2x+ 3|= 1- x is equivalent to x+ |2x+ 3|= 1 (add x to both sides). They have the same solutions.