1 - 2 1/3 < 2 1/6 solve this then desribe how it would look graphed on a number line

Answer 1

To solve the inequality 1 - 2 1/3 < 2 1/6, we first need to convert the mixed numbers into improper fractions.

1 can be written as 3/3, and 2 can be written as 12/6.

The inequality becomes: 3/3 - 7/3 < 12/6 - 1/6

Next, we need to find a common denominator, which in this case is 6.

The inequality simplifies to: 3/3 - 7/3 < 11/6.

Now, we can combine the fractions: (3 - 7)/3 < 11/6

-4/3 < 11/6

To compare these fractions, we need to find a common denominator, which is 6:

(-4*2)/3 < 11/6

-8/3 < 11/6

To simplify further, multiply both sides by 6 to eliminate the fractions:

(6 * -8)/3 < 11

-48/3 < 11

-16 < 11

This inequality is true, so the solution is -16 is less than 11. On a number line, we would represent this inequality by drawing a closed circle at -16 and an open circle at 11. Then, we would connect them with an arrow pointing towards the left to indicate that values less than -16 satisfy the inequality.