solve the following inequalities and represent the solutions graphically
1.) 2 + x < 6

Let's solve the inequality:

### Step 1: Solve the inequality
\[
2 + x < 6
\]
Subtract 2 from both sides to isolate \( x \):
\[
x < 6 - 2
\]
\[
x < 4
\]
Thus, the solution to the inequality is \( x < 4 \).

### Step 2: Graphical Representation
To graph the solution, imagine a number line:
- Mark the point \( 4 \) on the number line.
- Since the inequality is strict (\( < \)), use an open circle at \( 4 \) to indicate that \( x = 4 \) is not included.
- Shade all the values to the left of \( 4 \), as they satisfy the inequality \( x < 4 \).

### Graph:
On a number line, it would look like this:

```
---o------------------>
   4
```

Where the open circle at \( 4 \) and the arrow indicates that the solution includes all values less than 4.

Would you like further details, or have any questions?

### Related Questions:
1. What if the inequality were \( 2 + x \leq 6 \)?
2. How would you solve \( x - 3 > 2 \)?
3. What changes in the solution if the inequality is \( 2 + x > 6 \)?
4. Can you solve \( 2x + 3 \leq 7 \)?
5. How do you represent \( x \geq -2 \) graphically?

**Tip:** When solving inequalities, remember that the inequality direction flips if you multiply or divide by a negative number.

solve the following inequalities and represent the solutions graphically 1.) 2 + x < 6

Learn how to solve and graph the linear inequality 2 + x < 6 with a detailed step-by-step explanation. This problem focuses on basic algebraic principles and graphically representing inequalities on a number line. Ideal for students in Grades 6-8.

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