Question

find the range of values for x. (3x - 9)° 93° 26 27 ? < x <

Explanation:

Step1: Apply the Hinge - Theorem

If two sides of one triangle are congruent to two sides of another triangle, the longer third - side is opposite the larger included angle. Here, since \(27>26\), we have \(93^{\circ}>3x - 9^{\circ}\). Also, the measure of an angle must be greater than \(0^{\circ}\), so \(3x-9>0\).

Step2: Solve the inequality \(3x - 9>0\)

Add 9 to both sides: \(3x-9 + 9>0 + 9\), which simplifies to \(3x>9\). Then divide both sides by 3: \(x > 3\).

Step3: Solve the inequality \(93>3x - 9\)

Add 9 to both sides: \(93+9>3x-9 + 9\), so \(102>3x\). Then divide both sides by 3: \(x<34\).

Answer:

\(3 < x < 34\)