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# Solve 2x-7+3x=4x+2 Is there no solution, one solution or an infinite number?

I need the solution to the equation and how to know whether there is no solution, one solution or an infinite number?

### 1 Answer by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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2 X - 7 + 3X = 4X + 2

5X - 7 = 4X +2   ( simplify both sides)

5X - 4X = 2 + 7  ( move variable to one side and constants to other.)

### X = 9

Thank You for Your Quick Response.  Please show how the value x=9 works.  When I substitute the value 9 for x back in on both sides of the equation, I get an 48=38 so I need to know what I did wrong.  Thanks again!
3rd line goes like this:
5X - 7 = 4X +2

Now you subract 4X on both sides, and add +7 to both sides.

5X -4X +7 -7 = 4X - 4x +2 +7

X = 9                                     Instead of adding and subtracting quantities to both sides we say. Move
variable to one side and constants to other, and moving any quantity
from one side to other change the sign, which is equivalent of adding a
quantity to both sides.
Like
5X  - 7 = 4X +2

5X - 4X = 7 +2         like we moved 4X from right to left change the sign +4x t0 -4x
, and moved - 7 from left to right change the sign from -7 to +7.
So solution of Linear equation results in following 4 steps as follows:

1. Simplify both sides separately, combine like terms together.

2. After each sides be simplified and contain not more than 2 terms in each side.
3. Move constants to one side, and variables to other, change the sign in moving from one side                       to other.
4.  combine the like terms again after step 3.

The equation should be simplified to  mX = n ,    = m/n

Look at an example.

2 + 3 ( X + 5 ) = 4 ( X + 5 ) - 8

2 + 3X + 15 = 4X + 20 -8

3X + 17  =  4X + 12       ( End of 1st Step).

3X - 4X = -17 +12

- X = -5

X = 5

2X - 7 + 3X =  4X + 2

2( 9) - 7 + 3 (9) = 4 ( 9) +2

18  - 7 + 27 = 36 + 2

38  = 38