Question

Write two equations that can be used to solve the equation.

|6 + 7a| = 22

Answer 1

6 + 7a = 22 or 6 + 7a = -22

Explanation:

`|x|=a\iff x=a\ or\ x=-a,\ \text{for}\ a\geq0\\\\======================\\\\|6+7a|=22\iff6+7a=22\ or\ 6+7a=-22`

Solution:

`6+7a=22\ or\ 6+7a=-22\qquad\text{subtract 6 from both sides}\\\\7a=16\ or\ 7a=-28\qquad\text{divide both sides by 7}\\\\a=(16)/(7)\ or\ a=-4`

Answer 2

Answer:
6 + 7a = 22
-6 -7a = 22

Since the equation has an absolute value in it, the numbers underneath the radical can be positive or negative. That means the two equations that can be used to solve it are

6 + 7a = 22
And
-(6+7a) = 22
= -6 -7a = 22