How would you graph the inequality 3r+5>3r-2 on a number line?
I know first you have to solve for r, and I did that (5>-2). I'm having trouble putting it on a number line though.
To graph the inequality 3r + 5 > 3r - 2 on a number line, you need to follow these steps:
1. Solve for r: You correctly solved the inequality and found that 5 > -2. However, I think there might be a mistake because 5 is not greater than -2. The correct inequality should be 3r + 5 > 3r - 2, which simplifies to 7 > -2.
2. Identify the symbol: The inequality symbol ">" indicates that the solution lies to the right of the value, on the number line.
3. Draw a number line: Draw a horizontal line with an arrow on both ends representing all real numbers.
4. Mark a point: On the number line, make a small point to indicate the endpoint where the solution lies. Since our inequality is 7 > -2, we use 7 as the point.
5. Shade the region: Now, shade the region to the right of the point you marked. This represents all values of r that satisfy the inequality.
6. Add an open circle: Since the original inequality is greater than (>) and not greater than or equal to (≥), you will use an open circle on the number line right above the point you marked at 7. This indicates that the value 7 is not part of the solution.
So, on the number line, you will have an open circle above 7, and a shaded region to the right.