Question

solve for x: 2/5 + 3/5x = x +5/10

Answer: NO SOLUTION

Answer 1

@jim_thompson5910

Answer 2

the equation is

\[\Large \frac{2}{5} + \frac{3}{5x} = \frac{x+5}{10}\]

right?

Answer 3

Looking at the solutions, I think it is perhaps more likely to be
\[\frac{2}5 + \frac{3}{5}x = \frac{x+5}{10}\]

Answer 4

WolframAlpha.com came up with\[\frac{2}{5}+\frac{3}{5} x=x+\frac{5}{10} \]where x = -1/4

Answer 5

solution to mine is x = 1/5.

@InsanelyChaotic what is the correct form of the equation?

Answer 6

@whpalmer4 the way @jim_thompson5910 wrote it was correct

Answer 7

well

\[\Large \frac{2}{5} + \frac{3}{5x} = \frac{x+5}{10}\]

has two solutions, so the answer isn't "no solutions"

Answer 8

so double check your work

Answer 9

-1/4 and -2?

Answer 10

Multiply through by 10x, giving
\[4x + 6 = x(x+5)\]\[4x+6=x^2+5x\]\[x^2+x-6=0\]Can you factor that?

Answer 11

no...

Answer 12

Well, you'll have \[(x-a)(x+b)\]where a*b =6 and the difference between a and b is 1. Can you think of a pair of numbers that makes that true?

Answer 13

What are the factors of 6?

Answer 14

3

Answer 15

That's one factor, what's another?

Answer 16

12

Answer 17

Um, no. 12 is not a factor of 6. Factors are the numbers which when multiplied together give you the number you are factoring. What do you have to multiply 3 by to get 6?

Answer 18

___ * 3 = 6
What goes in the blank?

Answer 19

2

Answer 20

Good. Other factors of 6 are 1 and 6. So, we need two of those factors which when multiplied give 6, and are only 1 apart (difference is 1). Make your selection, please...

Answer 21

Choices are 1, 2, 3, 6

Answer 22

2

Answer 23

We need two numbers. Not one. The two numbers must multiply to 6, and the difference between them must be 1.

Answer 24

2 an 3

Answer 25

Very good.

So, the middle term is +x, so we need the bigger of the two to be the one with the plus sign (it will be 3x - 2x = 1x):

Our equation factors to\[(x+3)(x-2)= 0\]For a product to be 0, one or more of the things being multiplied must be 0. We don't know which, and we want to find all the possible values of x that make that true. So, we set each one equal to 0 and solve for x.

\[x+3=0\]
\[x-2=0\]
What are the two values of x that satisfy those equations? Those are the solutions to this problem.

Answer 26

Checking our factoring:
\[(x+3)(x-2) = x(x-2) + 3(x-2) = x^2 -2x + 3x -6 = x^2 + x -6\checkmark\]