the sum of two-thirds of a number and eight is equal to the difference of seven-thirds of the same number and two

Question

the sum of two-thirds of a number and eight is equal to the difference of seven-thirds of the same number and two

 

Answer 1

(2/3)x + 8 = (7/3)x - 2

 

Let's clear the fractions.  Multiply everything by 3

 

2x + 24 = 7x - 6

 

subtract 2x from both sides

 

24 = 5x - 6

 

add 6 to both sides

 

30 = 5x

 

divide both sides by 5

 

6 = x   ....  Note that this is the same as x=6