To solve the inequality 2 + 4w ≥ 7, we first need to isolate the variable w.
1. Start by subtracting 2 from both sides of the inequality:
2 + 4w – 2 ≥ 7 – 2
This simplifies to:
4w ≥ 5
2. Next, we divide both sides by 4 to solve for w:
w ≥ 5/4
Now we have our solution: w is greater than or equal to 5/4.
To graph this solution on a number line:
- Draw a number line.
- Locate the point 5/4, which is the same as 1.25.
- Since the inequality is greater than or equal to (≥), we place a closed circle at 5/4 to indicate that this point is included in the solution.
- Then shade the line to the right of 5/4 to show that w can take any value greater than 5/4.
This graphical representation gives a clear visual of the solution to the inequality.