Question

look at the diagram. which equation can be used to solve for x? 11x - 6 = 71 2x + 3x = 71 7x - 6 = 71 2x + 3 = 71 solve for x. x =

Explanation:

Step1: Analyze angle - relationship

According to the angle - addition postulate, the sum of the two adjacent angles \(2x^{\circ}\) and \((9x - 6)^{\circ}\) is equal to \(71^{\circ}\). So the equation is \(2x+(9x - 6)=71\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+9x-6 = 11x-6\). So the equation becomes \(11x - 6=71\).

Step3: Solve the equation for \(x\)

Add 6 to both sides of the equation: \(11x-6 + 6=71 + 6\), which simplifies to \(11x=77\). Then divide both sides by 11: \(x=\frac{77}{11}=7\).

Answer:

The equation is \(11x - 6 = 71\), \(x = 7\)