Question

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

Answer 1

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!