Now, that we know the perimeter, we can create an inequality. The perimeter must be less than 30 inches and greater than 20 inches.
30>2(x+2+6)>20
b To represent the inequality graphically, we will need to solve it first. We can do this by breaking the inequality into two parts and isolating the variable in each.
30 > 2(x+2+6)
and
2(x+2+6) > 20
Now, we can solve. Let's start with 30 > 2(x+2+6).
We found that x can be less than 7 and greater than 2. Because these inequalities are strict, we need open circles at 2 and 7 on the number line and we can shade between the circles.
c Now, that we have found the possible values for x, we can represent the possible perimeters of the triangle on a number line. Let's start by finding the perimeter of the triangle.
If x=2, the perimeter would be 16 inches however, we know that x>2. This means that the perimeter of the triangle will be greater than 16. Now, we can check for when x=7.
If x=7, the perimeter would be 31 inches. However, we know that x<7. Therefore, the perimeter of the triangle will be less than 31. Since x can be any value between 2 and 7, the perimeter of the triangle can be any value between 16 and 31.
16 < Perimeter_(Triangle) < 31
These inequalities are also strict so, in the graph, we place open circles on 16 and 31. Then, we will shade between them.
