Question

Solve the inequality. Graph the solution set. 2r−9≤−6

Answer 1

Hey!


The first step to solving this inequality is to change the equation. We'll change the equation by adding plus nine to both sides of the equation. This will help us get 2r on its own.

Original Equation :
2r - 9 ≤ -6

New Equation {Added Plus 9 to Both Sides} :
2r - 9 + 9 ≤ -6 + 9

Now we'll simplify the equation by solving -9 + 9 and -6 + 9.

Old Equation :
2r - 9 + 9 ≤ -6 + 9

New Equation {Old Equation Simplified} :
2r ≤ 3

Once again we'll have to change the equation. We'll do this by adding divide both sides by two. This will give us the variable ( r ) on its own.

Old Equation :
2r ≤ 3

New Equation {Added Divide 2 to Both Sides} :
$\frac{2r}{2}$  ≤  $\frac{3}{2}$

Now we simplify.

Old Equation :
$\frac{2r}{2}$  ≤  $\frac{3}{2}$

New Equation {Old Equation Simplified} :
r ≤  $\frac{3}{2}$

Now, that is, in fact, the solution but since I'm not sure which form you need, I've written it in other forms as well.

Solution →   r ≤  $\frac{3}{2}$

Decimal →   1.5

Interval Notation →   $(-$ ∞$, \frac{3}{2} )$

Below, I have also attached a graph that shows how this inequality should be graphed.

Hope this helps!


- Lindsey Frazier ♥

Answer 2

We have that

2r−9≤−6------> 2r ≤ -6+9-------> 2r ≤  3-----> r ≤ 1.5

the solution is the interval  (-∞, 1.5]

using a graph tool
see the attached figure