Question

1. solve: a) -9x - 4 = 2 b) $\frac{x - 4}{5}=\frac{-3}{7}$ 5) which theorem states that these lines are parallel? a) alternate interior angles theorem b) alternate exterior angles theorem c) alternate exterior angles converse d) alternate interior angles converse

Explanation:

a)

Step1: Add 4 to both sides

$-9x - 4+4=2 + 4$
$-9x=6$

Step2: Divide both sides by -9

$x=\frac{6}{-9}=-\frac{2}{3}$

Step1: Cross - multiply

$7(x - 4)=5\times(-3)$
$7x-28=-15$

Step2: Add 28 to both sides

$7x-28 + 28=-15+28$
$7x = 13$

Step3: Divide both sides by 7

$x=\frac{13}{7}$

The converse of the alternate exterior angles theorem states that if alternate exterior angles are congruent, then the lines are parallel. Here, the 132 - degree angles are alternate exterior angles.

Answer:

$x =-\frac{2}{3}$

b)