"Solving Equations with the variable on each side." The first equation is 3k - 5 = 7k - 21. We are asked to "Solve each equation. Check your solution." The samples in her textbook are quite useless. Any ideas? Thank you.
One thing to remember, always, is that what you do to one side you must do to the other. That will be the key to success in these problems. Next, you want to solve for k; therefore, your goal is to get the variable (in this case k) on one side alone, and the numbers on the other.
3k - 5 = 7k - 21
+5 +5 <- I am going to add 5 to get rid of it on the left side
3k = 7k - 16 <- negative 5 + positive 5 = 0, negative 21 + positive 5 = negative 16
So, you have the above equation and now you need the variable (k) on a side on its own
3k = 7k - 16
-7k -7k <- subtract 7k from both sides
-4k = -16 <- proceed to divide both sides by -4 and you end up with k=4
Check: 3(4) - 5 = 7(4) - 21
12 - 5 = 28 - 21
7 = 7
Hope that made sense! Hard to explain math problems via answer box :)