Which of the following is a solution for the above equation

lucasdachequi
|3(-2.5) - 3| = |-7.5-3| = |-10.5| = 10.5..... not 4.5

Step 1: you can find the critical points on the number line, below which and above which the sign of the quantity inside the Modulus will change

|x - (-2)| + 2 |x - (-3)| + 3 |x - (+1)| = 12

The critical points: x = -3 , -2 , +1


{—————(-3)————(-2)—————(+1)——}

2nd) if you look at the answer choices, answers B, C, D, and E all fall with the range of greater than -2 and less than or equal to +1

Only answer A falls within a different range:

-3 </= x < -2

So let’s open the absolute value expressions according to this assumed range (if the answer doesn’t match A, then we can open the expressions according to the other range):

- (x + 2) + 2x + 6 - (3x - 3) = 12

-x - 2 + 2x + 6 - 3x + 3 = 12

-2x + 7 = 12

-2x = 5

X = 5 / -2 = (-) 5/2

Answer A

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\(|x+2|+|2x+6|+|3x-3|=12\)

Which of the following is a solution for the above equation

|x+2|+|2x+6|+|3x-3|=12

-3, -2, 1

Case 1: x<-3
-x -2 -2x - 6 - 2x + 3 = 12
-5x = 17
x = = -17/5 < - 3

Case 2: -3<=x<-2
-x -2 + 2x + 6 -3x + 3 = 12
-2x = 5
x = - 5/2

IMO A

I'm not quite understanding why you switch signs for one term over the others and how you're able to do this. Why don't you have to switch signs for all terms?

In case one it would be -3x + 3 right , so x = -17/6

The last option 5/3 is out of that range, so we have two choices A and E. Of these two we can plug any one value and check.