Question

Find the exact solution of the equation:
|7x-3|=|7x+6|
I'm not so sure how to do this. I've tried -(7x-3)=7x+6 but I don't think its right...

Answer 1

its correct but incomplete

|a| = |b|

---> |a| = b, |a| = - b
which gives

a=b, a=-b

Answer 2

so,
|7x-3|=|7x+6|
----->
7x-3=-(7x+6)
7x-3=7x+6

Answer 3

So do I try solve those two?

Answer 4

yes

Answer 5

I've solved 7x-3=-(7x+6) which is x=-3/14
but how do I solve 7x-3=7x+6?
Wouldn't 7x-7x=0?

Answer 6

yes,
which means that has no solution.

Answer 7

and -3/14 is the only solution :)

Answer 8

Oh ok, thanks a lot for your help!

Answer 9

There are three cases in different intervals of numbers.

First, both 7x - 3 and 7x + 6 are positive.
That is, 7x - 3 > 0 or x > 3/7.
In this interval, 7x - 3 = 7x + 6. No solution.

Second, both have opposite signs.
That is, 7x - 3 < 0 but 7x + 6 > 0. Or x < 3/7 but x > -6/7.
-(7x - 3) = 7x + 6.
-3/14 just so happens to be in this interval.

Answer 10

If we had some other solution, it wouldn't be considered. Next time, try plugging in your answer. These questions may be tricky!

Answer 11

I understand, thanks for telling me.