To solve the inequality 2x + 6 < 6x + 2 + 8, we first simplify the right side:
- Combine like terms on the right:
- 6x + 2 + 8 becomes 6x + 10.
Now, we can rewrite the inequality:
2x + 6 < 6x + 10
Next, we want to get all the terms involving x on one side and the constant terms on the other side. We can do this by subtracting 2x from both sides:
- 2x + 6 – 2x < 6x + 10 - 2x
- This simplifies to:
- 6 < 4x + 10
Now, we subtract 10 from both sides:
- 6 – 10 < 4x + 10 - 10
- This simplifies to:
- -4 < 4x
Next, we divide both sides by 4:
- -4/4 < 4x/4
- This simplifies to:
- -1 < x
Thus, the solution is:
x > -1
Now, let’s represent this solution on a number line:
- Draw a number line with 0 in the center and include -1 as a marked point.
- At -1, use an open circle to indicate that -1 is not included in the solution set.
- Shade the line to the right of -1 to show all numbers greater than -1 are included in the solution.
This visual representation makes it clear that the solution set is all the numbers greater than -1.