Choose the correct solution and graph the inequality
y-1/3>1/8
To solve the inequality y - 1/3 > 1/8 and graph it, we first isolate the variable y on one side.
Starting with:
y - 1/3 > 1/8
We want to get rid of the fraction on the left side by adding 1/3 to both sides:
y - 1/3 + 1/3 > 1/8 + 1/3
This simplifies to:
y > 1/8 + 1/3
To add fractions, they must have a common denominator. The least common denominator (LCD) of 8 and 3 is 24. Convert each fraction:
y > (1 × 3)/(8 × 3) + (1 × 8)/(3 × 8)
y > 3/24 + 8/24
Now that they have common denominators, we can add the numerators:
y > 3/24 + 8/24
y > 11/24
The solution to the inequality is:
y > 11/24
To graph this inequality on a number line:
1. Draw a horizontal line representing the values of y.
2. Identify the point corresponding to 11/24 on the number line.
3. As it's a strict inequality (not including the equality), we use an open circle to signify that 11/24 is not included in the solution.
4. Because y is greater than 11/24, we shade the number line to the right of the point.
Here's a simple representation of how the graph would look (Note that this is a text representation and might not be to scale):
```
| | | | | |
----|----|----|----|----|----|----> y
0 1/24 2/24 3/24 ... 11/24 ...
( )
^
|
Open circle at 11/24 and the line is shaded to the right
```
The shaded area to the right of the open circle indicates all the values of y that satisfy the inequality y > 11/24.