Answer:
[tex]-2/5 \text{ and } 6[/tex]
Step-by-step explanation:
So we have the equation:
[tex]|3k-2|=2|k+2|[/tex]
First, distribute the 2 into the absolute value:
[tex]|3k-2|=|2k+4|[/tex]
Definition of absolute value:
[tex]3k-2=(2k+4) \text{ or } 3k-2=-(2k+4)[/tex]
Left:
[tex]3k-2=2k+4[/tex]
Subtract 2k from both sides:
[tex]k-2=4[/tex]
Add 2 to both sides:
[tex]k=6[/tex]
Right:
[tex]3k-2=-(2k+4)[/tex]
Distribute the negative:
[tex]3k-2=-2k-4[/tex]
Add 2k to both sides:
[tex]5k-2=-4[/tex]
Add 2:
[tex]5k=-2[/tex]
Divide by 5:
[tex]k=-2/5[/tex]
So, our solutions are:
[tex]-2/5 \text{ and } 6[/tex]
