Could you help me solve these?

|2x - 3| = -17

|5x + 3| = 12

Question

Could you help me solve these?


|2x - 3| = -17

|5x + 3| = 12

turingtest · Answer

for the first one, what happens when you take the absolute value of a negative number?

anonymous · Answer

Doesnt it turn into a positive

turingtest · Answer

correct, so how can taking the absolute value of the left side leave us with -17 ?

anonymous · Answer

I dont know?

turingtest · Answer

the answer is you can't; it's impossible
hence the answer to the first problem is...?

anonymous · Answer

NO solution?

turingtest · Answer

correct

turingtest · Answer

for the next one, the fact that taking the absolute value of the left gives us 12 means that the left side is one of which two possible numbers?

anonymous · Answer

It would be a negative number

anonymous · Answer

Wouldnt you divide 5 from both sides then multiply the number by 3 and negative 3?

turingtest · Answer

no, what two numbers have an absolute value of 12?

anonymous · Answer

-12 and 12

turingtest · Answer

great, so solve the left side twice, once for each possibility

anonymous · Answer

I dont know how to do that

anonymous · Answer

You want to get x alone dont you?

turingtest · Answer

|5x + 3| = 12   means that either
5x + 3 = 12     or    5x + 3 = -12

turingtest · Answer

yes

anonymous · Answer

So you would divide 5 from both sides

turingtest · Answer

i would do that last

anonymous · Answer

So what should i do first?

turingtest · Answer

deal with the addition

anonymous · Answer

Subtract 3?

turingtest · Answer

yep

anonymous · Answer

Okay so for the equation with positive 12 it is 1.8

turingtest · Answer

sounds right

anonymous · Answer

Then for the second equation it is -3

turingtest · Answer

yep :)

anonymous · Answer

and thats all you need to do?

turingtest · Answer

that's it

turingtest · Answer

you would write the answer as$$x=\{-3,1.8\}$$

anonymous · Answer

So equation one had no solutions and equation two and 2 solutions?

turingtest · Answer

that's correct

anonymous · Answer

@TuringTest I have another questions about absolute values.. concerning the same thing we just went over

anonymous · Answer

-3|x - 3| = -6 with this equation right here.. What would i do with the negative 3 thats outside of the lines?

anonymous · Answer

Would i add that up in the end or what?

turingtest · Answer

no, you need to deal with that first
treat |x-3| as the thing you need to find. let's say y=|x-3|. the problem is then
-3y=-6

turingtest · Answer

simplify this to get
y=2     and now substitute back in
|x-3|=2