how do i begin to solve x over 3 plus 1 = x over 6

Question

what do i do with the 1?

Answer 1

Hi Sherry,

To solve for X you first want to get all the terms that have an X in them to one side of the equation -- in this case the easiest way to do that is to subtract X/3 from both sides.

This leaves you with 1 = X/6 - X/3, so you didn't have to do anything with the 1.

The next step is to get a common denominator on the right-hand side.  Since 6 is a multiple of 3 I will use 6 as my common denominator.  

• X/6 already has 6 as the denominator, so there is nothing for us to do there!
• X/3 is the same as 2X/6 since 3 goes into 6 twice, or 2 times.
• Thus the right-hand side is now X/6 - 2X/6

Now that you have a common denominator we can complete the subtraction on the right-hand side: X/6 - 2X/6 = -X/6

The equation is now 1 = -X/6.  To get the X by itself we can multiply both sides by -6

• 1 * -6 = -6
• -X/6 * -6 = X

This yields the result X = -6 as the final answer.  (Note there is certainly more than one approach to this problem.  If you would like to see alternate solutions feel free to respond.  I or someone else on here will be glad to provide one!)

Answer 2

x/3 + 1 = x/6

x/3 - x/6 = -1

2x/6 - x/6 = -1

2x - x = -6

x = -6