Video Transcript
A number is tripled and seven is
subtracted from the result. If the answer is 17, what is the
number?
The first thing we need to do here
is take this statement and turn it into a mathematical one. We have an unknown number. And to represent an unknown number,
we need a variable. It’s common to use the variable
𝑥. And our number is tripled. If we triple 𝑥, it becomes three
𝑥. Whatever this three 𝑥 is, seven is
subtracted from that. Because we don’t know what three 𝑥
is, we have to write three 𝑥 minus seven. And the answer is 17. So, we can say that three 𝑥 minus
seven equals 17.
If we start with this equation,
three 𝑥 minus seven equals 17, we need to work in the reverse order. The last thing we did to our number
was subtract seven. In order to reverse this operation,
we need to add seven. But in order to keep both sides of
the equation equal, we need to add seven to both sides based on the addition
property of equality. On the left, three 𝑥 minus seven
plus seven equals three 𝑥. And on the right, 17 plus seven
equals 24.
To undo the subtract seven, we
added seven to both sides. How would we then undo this tripled
value? If we remember that triple means
times three, to undo that, we would divide by three. We need to then divide by three on
both sides. Three 𝑥 divided by three equals
𝑥. 24 divided by three equals
eight. We can do this because of the
multiplication property of equality. Which says if we multiply or divide
by the same thing on both sides of the equation, the statement remains
equivalent. Using these two properties, we’ve
shown that 𝑥 equals eight.
In problems like this, it can be
worth it to check and make sure that’s true. If our number is eight, and it’s
tripled, eight times three equals 24. Seven is subtracted from that
result. 24 minus seven should equal 17. And it does. So, we’ve correctly identified the
missing number, which is eight.
