Question

1. (9x + 17) a (3x - 4) b (6x - 31) c x =

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((3x - 4)+(9x + 17)+(6x - 31)=180\).

Step2: Combine like terms

First, combine the \(x\) - terms: \(3x+9x + 6x=18x\). Then combine the constant terms: \(-4 + 17-31=-18\). The equation becomes \(18x-18 = 180\).

Step3: Solve for \(x\)

Add \(18\) to both sides of the equation: \(18x-18 + 18=180 + 18\), which gives \(18x=198\). Then divide both sides by \(18\): \(x=\frac{198}{18}=11\).

Answer:

\(11\)