please show me how to solve this problem - 1/2 + 2/3x>1/6 - 1/2x

Question

please show steps on how to solve this problem. thank you.

Answer 1

-½+⅔x>⅙-½x.

Multiply each term by 6:

-3+4x>1-3x,

7x>4, x>4/7 so the solution to this inequality is all x greater than 4/7.

CHECK

For x=1 we would expect the original inequality to be true because 1>4/7:

-½+⅔=-3/6+4/6=⅙;

⅙-½=1/6-3/6=-2/6=-⅓. ⅙>-⅓ so the inequality is confirmed to be true.

For x=½ we would expect the original equality to be false because ½<4/7:

-½+⅓=-3/6+2/6=-⅙;

⅙-¼=2/12-3/12=-1/12. -⅙=-2/12<-1/12 so the inequality is in fact false, as expected.

These checks demonstrate that the solution x>4/7 is true.