In this lesson we will learn how to create and solve mathematical sentences.  You may recognize a mathematical sentence as an equation. 
You will also see that the "process" of solving a mathematical sentence is just as important as the "solution".

 Model Problems

The first step in creating a mathematical sentence is to write a "let statement."

Let x = number of marbles that Jake has.

Let x + 7 = the number of marbles that Mary has.

Now we write the mathematical sentence (the equation).

                             x + (x + 7) = 45

Now we solve the mathematical sentence (the equation).

                2x + 7 = 45   (combine like terms)

                2x = 38      (subtract 7 from both sides of the equation)

                x = 19        (divide both sides of the equation by 2)

Jake has 19 marbles!
 

First let's write the let statement.  The let statement needs to tell us what we are looking for in the problem.  Since the question asks us to find " the number" then our let statement will look like this:

                  Let x = the number

Now we write the mathematical sentence (the equation).

                   12(x) + 9 = 105

Now we solve the mathematical sentence (the equation).

             12x +9 = 105

             12x = 96    (subtract 9 from both sides)

             x = 8       (divide both sides by 12)

The number we are looking for is 8.

Again, first we write the let statement:

     Let 4x - 1 = the length of a side of the square.

Now we write the mathematical sentence:

   (4x - 1) + (4x - 1) + (4x - 1) + (4x - 1) = 60

                        OR

             4 ( 4x - 1) = 60  (either one is fine!)

Now we solve the mathematical sentence:

           16x - 4 = 60  (simplify the equation) 

           16x = 64   (add 4 to both sides of the equation).

           x = 4      (divide both sides of the equation by 16).

Now, be careful. Go back and look at the problem as well as the let statement to remind you what we are looking for. 

The problem asks us to find the length of a side of the square.  And the let statement says that the length of a side is not x, but rather 4x - 1.

So we need to "plug in" the solution to our mathematical sentence into the expression we used to represent a side of the square.

    Since our solution tells us that x = 4

    4x - 1 means  4(4) - 1, or 16 - 1 = 15.

   The length of a side of the square is 15