Applying the SAS Inequality Theorem, the range of x is calculated as: -6 < x > 5.
What is the SAS Inequality Theorem?
To find the range of x, we need to apply the SAS inequality theorem, which states that, if two sides and the included angle of one triangle are congruent to those of another triangle, the triangle with the larger included angle will have a longer third side.
Thus, we have:
3x - 15 < 5x - 3 [this is because 32 < 26, comparing their corresponding sides]
5x - 3 > 3x - 15
5x - 3x > 3 - 15
2x > -12
x > -6
Since an angle is always greater than 0, we have:
3x - 15 > 0
3x > 15
x > 5
The range is therefore, -6 < x > 5