SOLUTION: Solving equations using more than one property. 3(r+4)=21, 3(r-4)=27

Question 74141: Solving equations using more than one property. 3(r+4)=21, 3(r-4)=27
Found 2 solutions by funmath, bucky:
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Solving equations using more than one property. 3(r+4)=21, 3(r-4)=27

To check, let r=3 and see if both sides equal:

We're right!!!!
:

To check, let r=13 and see if both sides equal:

We're right again!!!!
Happy Calculating!!!!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given the equation:
.
3(r+4)=21
.
We will solve this using the following properties:
.
Distributive multiplication
Addition or subtraction
Division
.
First let's do the distributive multiplication on the left side. Multiply 3 times each of the
terms in the parentheses to make the left side become:
.
3r + 12 = 21
.
Next our goal is to get all the numbers on one side of the equation and the variable term
on the other side. We can do this by getting rid of the 12 on the left side. So let's subtract
12 from the left side. But in an equation, whatever we do to one side, we must do the same
exact thing to the other side. So if we subtract 12 from the left side, we must also subtract
12 from the right side ... and this means we subtract 12 from 21 on the right side.
When we do this the equation becomes:
.
3r = 9
.
From this equation we can ask ourselves "if 3 r's are 9, what must 1 r be?" The way to do
this algebraically is to divide BOTH sides of this equation by 3. We'll use this division
property as follows. 3r divided by 3 is just r and 9 divided by 3 is 3. So our final answer
is r = 3.
.
You can check this answer by going back to the original problem and putting 3 into the
equation wherever you see an r. When you do the equation becomes:
.
3(3+4) = 21
.
Inside the parentheses you can add the 3 and the 4 to get 7. Then the problem becomes:
.
3*7 = 21
.
And since the left side equals the right side, the equation checks out OK as long as
we use our answer r = 3. So our answer is correct.
.
On to your second problem. You are given:
.
3(r-4)=27
.
Use the exact same process as we did before.
.
First distributive multiply to get:
.
3r - 12 = 27
.
This time, to eliminate the 12 from the left side add +12 to BOTH sides to get:
.
3r = 39
.
Finally divide both sides by 3 to get:
.
r = 13
.
Check it out as we did before. This time put 11 in for r in the problem:
.
3(r-4) = 27
.
3(13-4) = 27
.
You do the work and see if the left side equals the right side. If it does, then our
answer of r = 13 is correct.
.
Hope this helps you to understand that solving equations often requires you to apply a number
of different rules to get an answer.
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