Seven times a number is equal to 12 more than 3 times the number. Find the number.
Answers
Step-by-step explanation:
So now you've found out that the number is 3.
Write out all your working:
7
n
=
12
+
3
n
−
3
n
+
7
n
=
12
4
n
=
12
n
=
12
4
n
=
3
Answer:
n=3
Step-by-step explanation:
Make n as the unknown number.
7
×
n
=
12
+
3
×
n
actually
7
n
=
12
+
3
n
You can see that there are two different terms.
The terms that are alike are 7n and 3n.
You need to send either one term to the left or to the right.
I would choose the term with
n
to go on the left-hand side.
So, I would bring
3
n
to the left-hand side.
As you can see,
3
n
is being added by something (always refer to this when solving this type of equation). To send it to the left-hand side, it has to become subtracted (since it's the opposite of addition) and becomes
−
3
n
as you put it on the left.
−
3
n
+
7
n
=
12
Simplify, if possible.
There are two terms with
n
on the right-hand side, so you have to add them up.
What is
−
3
n
+
7
n
??
Yeah, it's positive
4
n
.
So now you have
4
n
=
12
left.
How do you solve
4
n
=
12
to find
n
??
As you can see,
n
is being multiplied by 4 on the left-hand side, you want to send 4 to the right-hand side.
So what is the opposite of multiplication??
Yes! It's division.
Send
4
to the right-hand side and it becomes divided by
12
.
n
=
12
4
Final step,
What is 12 divide 4?
Yeah! It's 3, huh? Easy as that.
n
=
3
So now you've found out that the number is 3.
Write out all your working:
7
n
=
12
+
3
n
−
3
n
+
7
n
=
12
4
n
=
12
n
=
12
4
n
=
3