I need to find the n umber

## the product of twice a number and two is the same as the difference of three times the number and 7 over 9. find the number

# 2 Answers

Try to break off a word or two at a time.

the

productof twice a number and two is the same as the difference of three times the number and 7 over 9. find the number

Product means multiplication, so you need a multiplication sign *****. Now find what you're multiplying. There are two things being multiplied together:

the product of

twice a numberandtwois the same as the difference of three times the number and 7 over 9. find the number

Whenever you see "a number", make up a variable. Let's use **
x**. When you see "twice" that means

**2 ***. so now we have

**2 ***.

*x*The other number being multiplied is **2**.

Let's put all that together.

theis the same as the difference of three times the number and 7 over 9. find the numberproduct of twice a number and two

We can rewrite all of those words as **( 2 *
x ) * 2**.

Now let's look at the next chunks.

( 2 *

x) * 2is the same asthe difference of three times the number and 7 over 9. find the number

When you see "is the same as", that usually means an equals sign **
=**. Now we look at what comes after the equals sign.

( 2 *

x) * 2 =the differenceof three times the number and 7 over 9. find the number

"The difference" means a minus sign **-**. We need two things for subtraction:

( 2 *

x) * 2 = the difference ofthree times the numberand7 over 9. find the number

"Three times" is **3 ***, and "the number" is the same variable* x* that we picked before. So "three times the number" is the same as

**3 ***.

*x*"7 over 9" is a fraction, **7/9**.

Let's put that part together.

( 2 *

x) * 2 = the difference ofthree times the number and 7 over 9. find the number

We can rewrite those words as **( 3 * x ) - ( 7/9 )**.

Now our problem looks like this:

( 2 *. find the numberx) * 2 = ( 3 * x) - ( 7/9 )

And that's algebra.

**( 2 * x ) * 2 = ( 3 * x ) - ( 7/9 )**

Since the left hand side is all multiplication, you can move around the factors and parentheses, which is good, since you know what
**( 2 * 2 )** is and can simplify that part of the equation.

**( 2 * 2 ) * x = ( 3 * x ) - ( 7/9 )**

**4 * x = (3 * x) - ( 7/9 )**

When we're doing algebra with variables like * x*, we can just decide not to write the multiplication signs. Then our equation would look like:

**4x = 3x - 7/9**

Put the mulitples of x on one side of the equation. One way to do that would be:

**4x - 3x = - 7/9**

Then combine like terms:

**x = - 7/9**

#### So we found the number! It's **-7/9**!

Let x represent the number you are looking for.

Then the first part, which states that the product of twice a number (x) and two, would end up looking like the following:

(2*x) * (2) = (2*2) * x = 4x

For the second part, which states that the difference of three times the number (x) and 7 over 9 (7/9), you would end up at the following:

(3*x) - (7/9) = 3x - (7/9)

Since it says that the first part (4x) is the same as the second part (3x - (7/9)), then you would set these two equations equal to one another and solve for x.

That is, 4x = 3x - (7/9)

Combine like terms and separate them to one side of the equation; in this case, subtract 3x from both sides of the equation....

4x - 3x = 3x - 3x - (7/9) ===> 1x = 0 - (7/9) ===> x = -7/9