x - 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 x - 2 1/3 < 2 1/6, let's first find a common denominator for the fractions on both sides of the inequality. The common denominator for 3 and 6 is 6. Converting the mixed numbers to improper fractions, we have:

x - 7/3 < 13/6

Next, we need to get rid of the fractions by multiplying both sides of the inequality by 6:

6(x - 7/3) < 6(13/6)
6x - 14 < 13

Now, isolate x by adding 14 to both sides:

6x < 27

Finally, divide both sides of the inequality by 6:

x < 4.5

So, the solution to the inequality is x < 4.5.

To graph this on a number line, plot an open circle at 4.5 to represent that x is not included in the solution. Then shade the region to the left of 4.5, indicating that any value less than 4.5 satisfies the inequality. The graph would look like this:

<----------------o--->
-∞ 4.5 +∞

The open circle at 4.5 indicates that x is less than but not equal to 4.5. The shaded region to the left represents all the values that make the inequality true.