Question

# Describe the possible values of x.

## The correct answer is: Hence, all numbers between 1.6 and 15 are possible values of x.

### Answer:

- Hints:

- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

b < a + c

c < a + b

- Step-by-step explanation:

- Given:

In triangle,

a = x + 11, b = 2x + 10, and c = 5x - 9.

- Step 1:
- First check validity.

According to triangle inequality theorem,

c - b < a < b + c,

(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)

3x - 19 < x + 11 < 7x + 1

First consider,

- Step 1:
- First check validity.

According to triangle inequality theorem,

c - b < a < b + c,

(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)

3x - 19 < x + 11 < 7x + 1

First consider,

- Step 1:
- First check validity.

According to triangle inequality theorem,

c - b < a < b + c,

(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)

3x - 19 < x + 11 < 7x + 1

First consider,

x + 11 < 7x + 1,

11 – 1 < 7x - x

10 < 6x

1.6 < x

Now, consider,

3x - 19 < x + 11

3x - x < 11 + 19

2x < 30

x < 15

therefore,

1.6 < x < 15

x < 15

- Final Answer:

Hence, all numbers between 1.6 and 15 are possible values of x.

- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

- Given:

- Step 1:
- First check validity.

- Step 1:
- First check validity.

- Step 1:
- First check validity.

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