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

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:

$5 \left(x - 2\right) = 30$

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

$5 x - 10 = 30$

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;

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

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

$x = \frac{40}{5}$

$\therefore x = 8$

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

I hope this helps!