Question

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

Explanation:

Step 1: Analyze the angle relationships

From the diagram, we can see that the sum of the angles \(2x^\circ\) and \((9x - 6)^\circ\) should be equal to \(71^\circ\)? Wait, no, actually, looking at the angle composition: the angle between \(SR\) and \(SQ\) is \(2x^\circ\), the angle between \(SQ\) and \(SP\) is \((9x - 6)^\circ\), and the angle between \(SR\) and \(SP\) is \(71^\circ\). So, by the angle addition postulate, \(2x+(9x - 6)=71\). Let's simplify this: \(11x-6 = 71\). So the equation is \(11x - 6=71\).

Step 2: Solve the equation \(11x - 6 = 71\) for \(x\)

First, add 6 to both sides of the equation:
\(11x-6 + 6=71 + 6\)
\(11x=77\)

Then, divide both sides by 11:
\(x=\frac{77}{11}\)
\(x = 7\)

Answer:

The equation to solve is \(11x - 6 = 71\) and \(x=\boxed{7}\)