Which of the following shows the graph of the solution to x+1 2/3>4 ?(1 point)

Answer 1

To find the solution to the inequality \( x + \frac{5}{3} > 4 \), we first need to isolate \( x \).

Starting with:
\[ x + \frac{5}{3} > 4 \]

Subtract \(\frac{5}{3}\) from both sides:
\[ x > 4 - \frac{5}{3} \]

Convert 4 to a fraction with a denominator of 3 to subtract:
\[ 4 = \frac{12}{3} \]

So the inequality becomes:
\[ x > \frac{12}{3} - \frac{5}{3} \]
\[ x > \frac{7}{3} \]

Therefore, the solution to the inequality \( x + \frac{5}{3} > 4 \) is:
\[ x > \frac{7}{3} \]

To graph this on a number line, you would:

1. Identify \(\frac{7}{3}\) (which is approximately 2.33) on the number line.
2. Draw an open circle at \(\frac{7}{3}\), indicating that \(\frac{7}{3}\) is not included in the solution.
3. Shade the number line to the right of \(\frac{7}{3}\), indicating all numbers greater than \(\frac{7}{3}\) are part of the solution.

So, the graph of the solution will have:
- An open circle at \(\frac{7}{3}\).
- A shaded region extending to the right from \(\frac{7}{3}\).

Answer 2

can you show me how it looks

Answer 3

Sure! Here's a textual representation of what the graph of the solution to the inequality \(x > \frac{7}{3}\) looks like on a number line.

```
Number Line:
<---|----|----|----|----|----|----|----|----|---->
1 2 3 4

Location of \(\frac{7}{3}\) (approximately 2.33):
<---|----|----(2.33)----|----|----|----|----|---->
1 2 3 4

Graph Representation:
<---|----|----(o)====>===========================>
1 2 3 4
```

Explanation:
1. Identify \(\frac{7}{3}\) (approximately 2.33) on the number line.
2. Place an open circle `(o)` at \(\frac{7}{3}\) to indicate that \(\frac{7}{3}\) itself is not included in the solution.
3. Shade the line to the right (indicated by the `====>` sign) of \(\frac{7}{3}\) to show all numbers greater than \(\frac{7}{3}\) are included in the solution.

This graphical representation shows that:
- The solution includes all numbers to the right of \(\frac{7}{3}\).
- The open circle at \(\frac{7}{3}\) indicates the boundary is not included.

If you have access to graphing tools or graph paper, you can make the number line and indicate \(\frac{7}{3}\) more precisely between 2 and 3.

Answer 4

can you make it more clearer

Answer 5

Certainly! Let's create a clearer and more detailed representation of the number line and the graph of the solution:

```
1 2 3 4
|-------|-------|-------|-------|
2.33 (≈ 7/3)
```

Now, let's show how to graph \( x > \frac{7}{3} \):

```
1 2 2.33 3 4
|-------|-------(o)=====>-------|
```

Explanation:
- The vertical bars `|` represent integers on the number line.
- The notation `2.33` represents where \(\frac{7}{3}\) is approximately located.
- An open circle `(o)` is placed at \(\frac{7}{3}\), indicating that the point \(\frac{7}{3}\) is not included in the solution.
- The `=====>` drawn to the right of the open circle represents all numbers greater than \(\frac{7}{3}\), extending indefinitely.

To present it even more clearly, here is another representation with additional context:

```
Numbers: ... 1 2 2.33 3 4 ...
----|-------|-------(o)======>-------|----->

Graph: |-------|-------|-------| | ...
```

This representation incorporates the essential elements:
- `...` indicates the number line extends indefinitely.
- The numbers `1, 2, 3, 4` help to locate \(\frac{7}{3}\) (approx. 2.33).
- `=====>` with an open circle `(o)` at 2.33 shows that all numbers greater than \(\frac{7}{3}\) are included, excluding \(\frac{7}{3}\) itself.