Question

1. a student said that when x = 6, a || b. what error did the student likely make? for what value of x is a || b? (5x + 12)° (7x)°

Explanation:

Step1: Recall parallel - line property

When two lines \(a\) and \(b\) are parallel, the corresponding angles are equal. Here, the angles \((5x + 12)^{\circ}\) and \((7x)^{\circ}\) are corresponding angles. So, we set up the equation \(5x+12 = 7x\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides of the equation \(5x + 12=7x\). We get \(12=7x - 5x\), which simplifies to \(12 = 2x\). Then divide both sides by 2: \(x=\frac{12}{2}=6\). But the student likely just assumed \(x = 6\) without proper justification. To find the correct value of \(x\) for \(a\parallel b\), we solve the equation based on the parallel - line angle relationship.
\[

$$\begin{align*} 5x+12&=7x\\ 12&=7x - 5x\\ 12&=2x\\ x& = 6 \end{align*}$$

\]
The error the student likely made was assuming \(x = 6\) without using the property of corresponding angles for parallel lines. The correct value of \(x\) for which \(a\parallel b\) is found by setting the corresponding angles equal.

Answer:

The student likely made the error of assuming \(x = 6\) without using the property of corresponding angles for parallel lines. The value of \(x\) for which \(a\parallel b\) is \(x = 6\).