Answer:
[tex]q \in \{\frac{-4}{3},-5\}[/tex]
Step-by-step explanation:
If this has at least one solution then it will come from either 4q+9=2q-1 or from 4q+9=-(2q-1).
Let' solve the first:
4q+9=2q-1
Subtract 2q on both sides:
2q+9=-1
Subtract 9 on both sides:
2q=-10
Divide both sides by 2:
q=-5
Let's check it into the original equation:
|4(-5)+9|=|2(-5)-1|
|-20+9|=|-10-1|
|-11|=|-11|
11=11
So q=-5 checks out as a solution.
Let's solve the other equation:
4q+9=-(2q-1)
Distribute:
4q+9=-2q+1
Add 2q on both sides:
6q+9=1
Subtract 9 on both sides:
6q=-8
Divide both sides by 6:
q=-8/6
Reduce:
q=-4/3
Let's check it into the original equation:
|4(-4/3)+9|=|2(-4/3)-1|
|-16/3+9|=|-8/3-1|
|11/3|=|-11/3|
11/3=11/3
So q=-4/3 also checks out since both sides are the same when plugging in q=-4/3.
