# Can you please help me solve this equation and explain how you got the answer? Thank you! Solve Equation: |2x+3|=|x-6|?

### 2 Answers

- BebeLv 45 years agoFavorite Answer
|2x+3|=|x-6|

As each term |a+b| has 2 scenarios (a+b) or –(a+b), 2 terms will have 4 possible scenarios:

(a) Both positive

2x+3 = x-6 → x = -9

(b) LHS negative

-(2x+3) = x-6 → x = 1

(c) RHS negative

2x+3 = -(x-6) → x = 1

(d) Both negative

-(2x+3) = -(x-6) → x = -9

Since both (a) & (d) are the same mathematically, and (b) & (c) are the same, all you need is 2 scenarios:

(i) make both sides the same sign ((a) or (d)), or

(ii) change the sign of one side ((b) or (c)).

GRAPH

http://www.mathsisfun.com/data/function-grapher.ph...

Enter the following to plot:

y = abs(2x+3)

y = abs(x-6)

There will be 2 intersection points, where x=1 and x=-9.

.

- hayharbrLv 75 years ago
Obviously, if 2x + 3 = x - 6 (with no absolute value bars), then the absolute values would be equal too.

So one answer comes from that equation.

2x + 3 = x - 6

-x - 3.. -x - 3

--------------------

x = -9

However, if either part is the opposite of the other part, that would work too. So make one part be its opposite and solve that equation as well.

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

-2x - 3 = x - 6

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

2x + 3 = -x + 6

Thanks I understand how to get the -9 but how are you getting 1? If you could explain that part further I'd really appreciate it!