Can you please help me solve this equation and explain how you got the answer? Thank you! Solve Equation: |2x+3|=|x-6|?
- BebeLv 45 years agoFavorite Answer
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)).
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