Question

In △pqr, pq = 3x + 1, qr = 2x − 2, and pr = x + 7. Determine the range of possible values of x.

A) x > 1
B) x < 5
C) x > -3
D) x < 10

Answer 1

To determine the range of possible values of x in the triangle △pqr, we need to consider the given lengths of the sides pq, qr, and pr. The range of possible values of x is x > 2.

Step-by-step explanation:

To determine the range of possible values of x in the triangle △pqr, we need to consider the given lengths of the sides pq, qr, and pr. The range of possible values of x can be found by solving the inequalities formed by the lengths of the sides.

Given:

pq = 3x + 1

qr = 2x - 2

pr = x + 7

We know that the lengths of the sides of a triangle satisfy the triangle inequality theorem which states that the sum of the lengths of any two sides must be greater than the length of the third side.

So, we have the following inequalities:

(3x + 1) + (2x - 2) > (x + 7)

5x - 1 > x + 7

4x > 8

x > 2

And,

(3x + 1) + (x + 7) > (2x - 2)

4x + 8 > 2x - 2

2x > -10

x > -5

Therefore, the range of possible values of x is x > 2 and x > -5. Combining these two inequalities, we get x > 2.