Question

2x/3 + 1/4= x/6 - 1/2 solve for x

Answer 1

You need to bring all the x's to one side and all the numbers to the other:

2x/3 + 1/4= x/6 - 1/2

2x/3 - x/6 = -1/2 - 1/4

now lets multiply both sides by 3 to get rid of the 3 in the denominator of 2x/3

2x - 3x/6 = -3/2 - 3/4

now 3x/6 can simply down to x/2

2x - x/2 = -3/2 - 3/4

now notice we still need to get rid of the 2 in the denominator of x/2, so lets multiple everything by 2

4x - x = -6/2 - 6/4

3x = -3 - 6/4

Lets get a common denominator on the right side

3x = -12/4 - 6/4
3x = -18/4
3x = -9/2

divide both sides by 3

x = -9/(2*3)
x = -9/6
x = -3/2 (since both 9 and 6 can be reduced by 3)

Therefore x = -3/2

Hope this helped!