A number is doubled and then the product is increased by 6. This sum is then multiplied by -3, and the result is 54 greater than three times the opposite of the number. What is the number?

Answer 1

Let x represent the unknown number.

"A number is doubled": 2x "and the product is increased by 6": (2x +6).

"This sum is then multiplied by -3": (2x + 6)(-3)

"and the result is 54 greater than 3 times the opposite of the number": = 54 + 3(-x)

When you put everything together, you have (2x + 6)(-3) = 54 + 3(-x). Distribute and solve for x.

x = -24, and you can plug it in to verify and check to make sure the equation is indeed true.

Answer 2

Hi Alexis...I am a Wyzant tutor. Thank you for reaching out to Wyzant in helping you work to understand this kind of problem.

As a teacher, we work to help students learn to problem solve these kinds of questions. If I give you the answer, it really doesn't help you develop the skills with problems solving, especially when you have to take tests and you are all by yourself.

So here goes, I'm going to help you with addressing these kinds of problems.

Here is your problem:

A number is doubled and then the product is increased by 6. This sum is then multiplied by -3, and the result is 54 greater than 3 times the opposite of the number. What is the number?

Let's begin with what is the problems asking you to find? Some number right?

So...if we do some adding, some multiplying and other math stuff we should end up with some number. Something like this: add this, multiply this, subtract that..... equals (let's say) z

add this, multiply this, subtract that..... = z

We're going to take each of the parts of the problem and answer each section then put it all together,..like this"

A number is doubled (what does this mean?) 'a number is doubled'...so we multiply that number by 2 Like this some number (let's say a ) it looks like [2a]

Next

and then the product is increased by 6. (What does that mean?) It means we add 6 to it,

like this: our product [2a] + 6 = some number which is called what? (the sum)

This sum is then multiplied by -3, so we multiply our quantity (make sure you know what the word 'quality' means) by -3 which looks like: -3 x ( [2a] + 6 ) or -3( [2a] + 6 ) =

So do you see where I'm going with this problem solving?

I'm taking each segment of the problem and writing it out.

I'm going to give it to you to work out the rest for you to continue.

I am here to help...but as I mentioned...just solving it for you will not help when you have a different problem or when you are taking a test.

Contact me if you need any further help

Here you go....finish the rest....and the result is 54 greater than 3 times the opposite of the number.