Solve the inequality. Graph the solution set. 2r-9>-6
2r-9>-6
2r > 3
r > 1.5
To solve the inequality 2r - 9 > -6, we need to isolate r on one side of the inequality sign. Here's how we can do that step by step:
1. Add 9 to both sides of the inequality:
2r - 9 + 9 > -6 + 9
This simplifies to: 2r > 3
2. Next, divide both sides of the inequality by 2 (the coefficient of r) to solve for r:
(2r)/2 > 3/2
This simplifies to: r > 3/2
Thus, the solution to the inequality 2r - 9 > -6 is r > 3/2, which means that r is any value greater than 3/2.
Now let's graph the solution set on a number line to visually represent all the values of r that satisfy this inequality:
On the number line, plot an open circle at 3/2 to show that it is not included in the solution set because the inequality is strict (r > 3/2). Then, draw an arrow going to the right to indicate that the solution set includes all values greater than 3/2.
------->----------------
3/2
In this graph, all the values to the right of the open circle are solutions that satisfy the inequality 2r - 9 > -6.