Lisa and Jan found that 5 times the sum of a number and -2 equals 30. What is the number?

1 Answer
Apr 2, 2018

The number is 8

Explanation:

We need to form an equation from the question given. Let's call our unknown number x.

According to the question, we need to add -2 to x.
According to our operations rules, +- (or -+) gives -.

therefore x+(-2) is now: x-2

5 times the sum of this gives 30, so we use brackets to show this:

5(x-2)=30

We now have our equation and can solve. First, we expand the brackets (multiply each term by 5) to get:

5x-10=30

We group like terms together by moving the numbers to one side, and x's to the other.
We must add 10 to the LHS to get rid of the -10. What we do to the LHS, we must do to the RHS,so we add 10 to the RHS to get;

(5x-10+10=30+10) - (The 10 gets cancelled out)
5x=30+10
5x=40

Now, to get x, we must divide 5x by 5. We must also do this to the RHS, as shown above. We get:

x=40/5

therefore x=8

We can check this by starting with our answer in the question and obtaining 30.

I hope this helps!