Question

I need to solve the absolute value for |4q+9|=|2q-1| please help!!!

Answer 1

`q \in \{(-4)/(3),-5\}`

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.