Question

1. prove △prq≅△trs. 9. determine if each equation is a correct step in the process of solving 2(7). select yes or no for each equation. 14 + 10x - 6x = - 35 14 + 10x - 3x = - 35 7x = 49 14 + 7x = - 35

Explanation:

Step1: Prove triangle congruence

In \(\triangle PRQ\) and \(\triangle TRS\), we have \(\angle PRQ=\angle TRS\) (vertically - opposite angles are equal). Also, from the markings on the figure, \(PR = TR\) and \(QR=SR\). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle PRQ\cong\triangle TRS\).

Step2: Analyze the equations

Let's assume the original equation is \(2(7 + 5x-3x)=- 35\). First, simplify the left - hand side: \(2(7 + 2x)=14 + 4x
eq14 + 10x-6x\) and \(14 + 10x-3x
eq14 + 4x\). If we start from \(2(7 + 5x-3x)=-35\), we get \(2(7 + 2x)=-35\), then \(14 + 4x=-35\).
For \(14 + 10x-6x=-35\), simplifying the left - hand side gives \(14 + 4x\), so it could be a step if the original equation was manipulated correctly.
For \(14 + 10x-3x=-35\), simplifying the left - hand side gives \(14 + 7x\).
For \(7x = 49\), we don't know how it relates to the original equation \(2(7 + 5x-3x)=-35\) without more steps.
For \(14+7x=-35\), it could be a step in the simplification process.

14 + 10x - 6x=-35: Yes (assuming correct manipulation in the process)
14 + 10x - 3x=-35: No
7x = 49: No
14 + 7x=-35: Yes

Answer:

14 + 10x - 6x=-35: Yes
14 + 10x - 3x=-35: No
7x = 49: No
14 + 7x=-35: Yes