To solve the inequality 2x + 6 < 6x - 2 + 8, let’s start by simplifying both sides:
- Combine like terms on the right side: 6x – 2 + 8 becomes 6x + 6.
This gives us:
2x + 6 < 6x + 6
- Next, let’s get all terms involving x on one side and constant terms on the other.
Subtract 2x from both sides:
6 < 6x - 2x + 6
Which simplifies to:
6 < 4x + 6
- Now, subtract 6 from both sides:
0 < 4x
- This simplifies to:
- 0 < 4x or x > 0.
Thus, the solution set consists of all values of x that are greater than 0. On a number line, this is represented with an open circle at 0 and a line extending to the right towards positive infinity.
In conclusion, the number line that represents the solution set for the given inequality is one that shows all numbers greater than 0.