Question

Wich of following are solutions to |x+3|= 4x -7 Answer x= 10/3

Answer 1

Answer:

10/3

Step-by-step explanation:

|x+3|=4x-7

So |-(x+3)|=|x+3|

We are going to try out two cases:

-(x+3)=4x-7                              and    x+3=4x-7

-x-3=4x-7                                               3=3x-7

 -3=5x-7                                               10=3x

  4=5x                                                   x=10/3

  x=4/5

We are going to test out both because we could something that isn't actually a solution, this is called extraneous.

First thing I'm going to check is 4x-7 for it being positive.

4(4/5)-7=20/5-7=-15/5=-3 so 4/5 will not work because absolute value result can't be negative

4(10/3)-7=40/3-7=19/3 which is positive

checking |x+3| to see if is 19/3 for x=10/3 we see that is so that is the answer