Question 106113
{{{-5k-19=5-13k}}} 
When you solve an equation, you have to move all of the known terms (numbers) on one side and all of the unknown (k) terms on the other. 
Let's move all the k terms to the left hand side and all the non-k terms to the right hand side. 
Remember, whatever you do to one side of the equation, you have to do to the other side of the equation. 
{{{-5k-19=5-13k}}}
To get rid of the (-13k) on the right hand side, I have to add the additive inverse of (-13k). 
The additive inverse of x is -x be because x+(-x)=0. 
The additive inverse of (-13k) is -(-13k). 
Negative times negative is positive or -(-13k)=13k. 
Add 13k to both sides of the equation. 
{{{-5k-19=5-13k}}}
{{{-5k-19+13k=5cross(-13k)+cross(13k)}}}
{{{-5k-19+13k=5}}}
{{{13k-5k-19=5}}}
{{{8k-19=5}}}
To get rid of the -19 on the left hand side, use the additive inverse of -19. 
The additive inverse of (-19) is -(-19) or (19).
Add 19 to both sides of the equation.
{{{8k (cross(-19))+cross(19)=5+19}}}
{{{8k=24}}}
Now to get rid of the 8 in front of k, you need to use the multiplicative inverse of 8. 
The multiplicative inverse of x is 1/x since {{{x*(1/x)=1}}}.
The multiplicative inverse of 8 is 1/8. 
Multiply both sides of the equation by 1/8. 
{{{8k*1/8=24*1/8}}}
{{{(8/8)k=24/8}}}
{{{k=3}}}
Check your answer in your original equation. 
{{{-5k-19=5-13k}}} 
{{{-5(3)-19=5-13(3)}}}
{{{-15-19=5-39}}}
{{{-34=-34}}}
Good answer. 
Since you get an answer that makes sense, your solution is good. 
k=3.