(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

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- Aug 2nd 2013, 06:51 PM #1

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- Aug 2nd 2013, 06:58 PM #2

- Aug 2nd 2013, 07:08 PM #3

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- Aug 2nd 2013, 07:20 PM #4

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## Re: Question

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 $\displaystyle 2x+3\ge 0$, 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 $\displaystyle 2x+ 3\le 0$, 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.