My 13 year old daughter (8th grade) is stumped by her algebra homework.

Question

"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.

Answer 1

Karen,

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 :)

Answer 2

3k - 5 = 7k - 21

Right: what you do to one side you must do to the other!

(3k-5)+5-7k=(7k-21)+5-7k

(3k-5)+5-7k=(7k-21)+5-7k

3k-7k=-21+5

-4k=-16

(-1)(-4k)=(-1)(-16)

4k=16

4k/4=16/4

k=4

Check: 3(4) - 5 = 7(4) - 21
12 - 5 = 28 - 21
7 = 7

 

 

 

 

 

Answer 3

"Solve the equation with the variable on each side" just means that the variable will be on both sides of the equation. As a check to the above solution, let's solve the equation another way and see if we get the same answer.

Equation: 3k - 5 = 7k - 21

Our goal is to get the variable k all by itself. We need to:

1. Add 21 to both sides of the equation. We are adding 21 because the 21 is negative, so we are doing the opposite operation to get the 21 on the right to equal 0.  

3k - 5 = 7k - 21

    +21        +21

And we get. 3k + 16 = 7k

2. Now we want the variable to be on only one side of the equation. To do this, we must subtract 3k from both sides.

3k + 16 = 7k

-3k           -3k

So we get 16 = 4k

3. Our last step to get k all by itself is to divide 4 by both sides of the equation (because 4 is being multiplied by k, and division is the opposite operation).

16 = 4k

4        4

So we get 4 = k [Which is the same as the answer above, and has already been checked by the previous answerer.]