solve x - 2 1/3 < 2 1/6

Answer 1

To solve the inequality, we need to make sure that x is smaller than the right side of the inequality. We can start by converting the mixed numbers to improper fractions:

x - 7/3 < 13/6

Next, let's find the least common denominator (LCD) of the fractions on both sides, which is 6. We can multiply both sides of the inequality by 6 to clear the fractions:

6(x - 7/3) < 6(13/6)

6x - 14 < 13

Now, we can isolate the variable by adding 14 to both sides of the inequality:

6x - 14 + 14 < 13 + 14

6x < 27

Finally, we can solve for x by dividing both sides of the inequality by 6:

(6x)/6 < 27/6

x < 9/2

Therefore, the solution to the inequality is x < 9/2 or x is smaller than 4.5.