Twice the sum of a number and 6 is 5. What is the number?

2 Answers
Nov 19, 2017

The number is #–7/2#, which is also #–3.5#.

Explanation:

Let the unknown number be represented by the variable #n#.
Then we can translate the English to math:

#stackrel (2 xx) overbrace"Twice"" "stackrel((n+6))overbrace"the sum of a number and 6"" "stackrel = overbrace"is"" "stackrel 5 overbrace"5".#

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 #n# that would make this true. Since the sides are balanced, dividing both sides by 2 keeps the sides balanced:

#(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 #n# by itself on one side! We have just isolated #n#. All we need to do is simplify the right side.

The number 6 can be expressed as #12/2#, which give it the same denominator as #5/2#:

#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 #5-12#:

#n=(–7)/2#

(If you prefer decimals, you can now divide to get #–3.5# as an answer.)

Feb 16, 2018

The number is #3.5#

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 #" the sum of a number AND 6"#
#color(white)(wwwwwwwwwwwwwwwiwwwwwwwww)darr#
If we let our number be #x#, then we have: #(x+6)#

However we need to use #"TWICE"#' that sum, which means:
#color(white)(wwwwwwwwwwwwwwww)darr#
#color(white)(wwwwwwwwwwwwwwiww)2(x+6)#

The word 'IS' indicates the answer, it represents #=#

Now we can write the complete equation:

#" "2(x+6) = 5#

#2x+12 = 5#

#2x = 5-12#

#2x =-7#

#x = -3.5#

Check:

#2(-3.5+6)#
#=2(2.5)#
#=5#