Question

how to solve for |2x|+3x=10 using algebra?

Answer 1

If x > 0, then |2x| = 2x, hence the equation is
2x + 3x = 10
5x = 10
x = 2
As 2 > 0, this is consistent with the assumption x > 0 and therefore x = 2 is a solution.

Now analyze the case x < 0

Answer 2

would the x<0 part be like -(2x)<0, making the question -2x=-3x+10 and become x =-2?

Answer 3

If x < 0 then |2x| = -2x. Substitute that into the equation
|2x| + 3x = 10

Answer 4

so is the answer x=-2 right for that part?

Answer 5

and then make it become |2(-2)|+3(-2)=10?

Answer 6

No. For x < 0

|2x| + 3x = 10

is equivalent to

-2x + 3x = 10

Answer 7

so how would i find what x is = to?

Answer 8

C'mon. How do you solve that equation:
-2x + 3x = 10

Answer 9

-2x + 3x = x.

Answer 10

oh, um oh i see, x =10?

Answer 11

Yes. BUT, we started with x < 0 and have concluded that x = 10. That's a contradiction. Hence x = 10 is NOT a solution.

Therefore the only solution is the one we found for x > 0.

Answer 12

oh, ok thank you, i completely understand now :)