Twice the sum of a number and 6 is 5. What is the number?
2 Answers
The number is
Explanation:
Let the unknown number be represented by the variable
Then we can translate the English to math:
Our equation to solve is
#2(n+6)=5#
We consider this equation balanced—that is, we assume there is a number we could use for
#(2(n+6))/color(red)(2)=5/color(red)2#
Now our left-hand side has a multiplier of 2 and a divisor of 2. These cancel (because something times 2, then divided by 2, is just that something again).
#n+6color(white)(" "-6)=5/2#
Let's now take 6 away from both sides; once again, doing the same thing to both sides keeps the equation balanced:
#n+6color(red)(" "-6)=5/2color(red)(" "-6)#
The 6's on the left-hand side cancel (because if we start with something, then add 6, and then take away 6, we're back to the same something.)
#ncolor(white)(" "+6-6)=5/2-6#
We now have
The number 6 can be expressed as
#n=5/2-12/2#
Since the denominators are the same, we can now combine these two fractions into one:
#n=(5-12)/2#
Finally, we subtract
#n=(–7)/2#
(If you prefer decimals, you can now divide to get
The number is
Explanation:
The phrase 'The sum of' means you need to ADD numbers together.
Look for the word 'AND' which will indicate which numbers have to be added.
In this case it is
If we let our number be
However we need to use
The word 'IS' indicates the answer, it represents
Now we can write the complete equation:
Check: