Five times the difference of twice a number and three, decreased by the sum of the number and eight, equals 13

Question

Algebra 1 Word Problem, looking for number format.

Answer 1

Twice a number = 2n

 

Difference of twice a number and 3 = 2n - 3

 

Five times that = 5(2n + 3)

 

The sum of a number and 8 = n + 8

 

5(2n + 3) - (n + 8) = 13

 

 

 

 

Answer 2

Let x = the number

5(2x - 3) - (x + 8) = 13

10x - 15 - x - 8 = 13

9x - 23 = 13

9x = 36

x = 4

 

 

Answer 3

Hi Chase! The best way to understand this would be to break it down part-by-part!

 

Let’s start with “twice a number”. We will use a variable in place of “number”. This is saying twice that number, which means we are going to multiple our “number” by 2. Since we’re using a variable for “number” this will give us 2x. You can use any variable you’d like though!

 

Let’s look at another part: “the difference of twice a number and three”. If it says the difference of teo things it means we’re going to use subtraction between those two things. Our two things are “twice a number” and “three”. We know “twice a number” is 2x and we don’t have to do any thinking for “three” so we can plug those into our expression to give us: 2x-3

 

Our next part says ”five times” the expression we just found in the previous paragraph. For this, we have to do multiple the whole expression (2x-3) by 5. It will look like this: 5(2x-3)

 

The next part to look at is “the sum of the number and eight”. Sum means we’re using addition. We’ll have two things being added together. Our two things are the “number” and “eight”. This will just look like this since there is nothing being done to either thing: x+8

 

Then we’ll look at our final part that says “decreased by the sum of the number and eight”. We will use our expression found in the previous paragraph for this one. If something is being decreased by an expression, your expression will be subtracted from it.

 

We then need to look and see what (x+8) is being subtracted from. It says it’s being subtracted (or decreased) from “five times the difference of twice a number and three”. We already know that to be our expression 5(2x-3). So we know (x+8) is being subtracted from 5(2x-3). It will look like this:

5(2x - 3) - (x + 8)

 

All of that will equal 13, which looks like this:

5(2x - 3) - (x + 8) = 13

 

Now you solve for your variable:

5(2x -3) - (x + 8) = 13

10x - 15 - x - 8 = 13            Distribute the 5 to the first parenthesis and distribute the negative to the second parenthesis. 

9x - 23 = 13        Combine like terms

9x = 36               Add 23 to both sides

x = 4                   Divide by 9 on both sides

 

I hope this helped you! Let me know if you have any questions about any of it!