Question

WWhat is the solution to the equation 1/2 X +3 equals 2/3 X plus one

Answer 1

1/2x + 3 = 2/3x + 1....multiply everything by the common denominator of 6
3x + 18 = 4x + 6
3x - 4x = 6 - 18
-x = - 12
x = 12 <====

multiplying by the common denominator will get rid of the fractions

Answer 2

1/2x+3=2/3x+1
Your goal is to get all the x's on one side and all the numbers on the other side initially in order to solve for x.

1/2x+3=2/3x+1
subtract 1 from both sides
1/2x+2=2/3x
now you need to find the least common multiple of both denominators and multiply that number by both the numerator and demoninator

The least common multiple of both denominators is 6.
2 goes into 6 3 times, so you have to multiply the 1/2 by 3/3.
3 goes into 6 2 times, so you have to multiply the 2/3 by 2/2.

2=4/6x - 3/6x
2=1/6x
In order to divide the 1/6 fraction, you multiply both sides by its inverse of 6/1.

2(6/1)= 1/6 * 6/1x
12=x

You can check the answer to be sure it's correct.
1/2x+3=2/3x+1
2= 4/6(12) - 3/6(12)
2=8-6
2=2

Hope this helps!!  :)