x−2 1/3<2 1/6
To solve the inequality x - 2 1/3 < 2 1/6, we need to first convert the fractions into a common denominator.
The common denominator of 3 and 6 is 6.
2 1/3 can be converted to an improper fraction as follows:
2 * 3 = 6
6 + 1 = 7
So, 2 1/3 equals 7/3.
2 1/6 can be converted to an improper fraction as follows:
2 * 6 = 12
12 + 1 = 13
So, 2 1/6 equals 13/6.
Now, our inequality becomes:
x - 7/3 < 13/6
To get rid of the fractions, we can multiply each term in the inequality by 6 to eliminate the denominators:
6 * (x - 7/3) < 6 * (13/6)
6x - 14 < 13
Next, we can add 14 to both sides of the inequality to isolate the variable:
6x - 14 + 14 < 13 + 14
6x < 27
Finally, divide both sides of the inequality by 6 to solve for x:
6x/6 < 27/6
x < 4.5
Therefore, the solution to the inequality x - 2 1/3 < 2 1/6 is x < 4.5.