seven less than twice a number is the same as nine times the number

Question

seven less than twice a number is the same as nine times the number

Answer 1

let's break down which words mean which math operations. For example, for "same" I'm gonna use an equals sign, because in an equation the two sides are the same value.

 

seven less than twice a number = nine times the number

 

Where I see a number being used but I don't know what the number is, I'm going to use a variable, say x. In this case, it looks like they want the same variable used both times.

 

seven less than twice x = nine times x

 

"Twice" is an example of multiplications. "Nine times" is an even clearer example of multiplication.

 

seven less than 2*x=9*x

 

"Seven less than" means subtraction, but we have to make sure that we write it the correct way since subtraction is not commutative (the order changes the answer). In this case, if we want seven less than something, than we write something minus seven.

 

2x-7=9x

 

Hopefully that looks like something familiar. In this case we want to get all of our variables on the same side first, so subtract 2x from each side.

 

 2x-7=9x

-2x     -2x

-7=7x

 

Notice that the seven kept that negative sign in front of it. Now we have to think of a number x that when we multiply by seven, we get -7. Well, we can undo that multiplication by using an inverse operation. The inverse of multiplication is division, so let's divide both sides by 7

 

 -7=7x

 /7   /7

 -1=x

 

Here we get our solution, x=-1. Before we're done though, we should check that our answer makes sense. So let's go back to our original problem. Instead of "a number", I'm gonna test whether negative one makes the statement true.

 

Is it true that seven less than twice of negative one is the same as nine times negative one?

 

Well twice of negative one is negative two, and seven less than negative two is negative nine. That's the same as nine times negative one, so we're good!