Question

Write and solve an inequality or multiple inequalities to describe the possible values of x.

Answer 1

Answer:

x < 5.1

Step-by-step explanation:

Let's define:

• α: opposite angle to side 8 on the left triangle

• β: the angle between sides 8 and 10 on the left triangle

• x: missing side of both triangles

Using Law of Sines we can find x, as follows:

10/sin(95°) = 8/sin(α)

sin(α) = sin(95°)*8/10

α = arcsin(0.8) = 53.13°

β = 180° - 95° - 53.13° = 31.87°

x/sin(β) = 10/sin(95°)

x = 10/sin(95°)*sin(31.87°)

x = 5.3

On the other hand, we know that the addition of the two shorter sides of a triangle must be greater than the long side of the triangle. Therefore:

8 + 5.3 > 3x - 2

Solving:

8 + 5.3 + 2 > 3x  

15.3/3 > x

5.1 > x

or

x < 5.1

Answer 2

The value of x from the given inequality is x < 5.1

Inequality expressions

Inequality expressions are expressions that are not equal to each other

Given the following variables;

• α: opposite angle
• β: the angle between sides 8 and 10e
• x: missing side

Using the sine law to determine the value of x

10/sin(95°) = 8/sin(α)

sin(α) = sin(95°)*8/10

α = arcsin(0.8) = 53.13°

β = 180° - 95° - 53.13° = 31.87°

x/sin(β) = 10/sin(95°)

x = 10/sin(95°)*sin(31.87°)

x = 5.3

Also, using the rule that states that the addition of the two shorter sides of a triangle must be greater than the long side of the triangle. Hence;

8 + 5.3 > 3x - 2

8 + 5.3 + 2 > 3x  

15.3/3 > x

5.1 > x

x < 5.1

Hence the value of x from the given inequality is x < 5.1

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