Checking a Solution To check a solution to an equation, substitute the solution into the equation and verify that it makes the two sides of the equation equal. For example, to verify that = 10 is a solution to the equation 3(x 5) = 15, substitute 10 into the x − equation for and then verify that the two sides of the equation are equal. x As shown at right, = 10 is a solution to the equation 3(x 5) = 15. x − What happens when you do this check if your answer is incorrect? For example, try substituting = 2 into the same equation. The result shows that = 2 is not a solution to this x x equation. Investigation 9: Solving a Word Problem Math Notes Solving Problems with the 5D Process The 5D Process is an organized method to problems. The D’s stand for Describe/Draw, Define, Do, Decide, and Declare. An example of this work is shown below. Problem: The base of a rectangle is 13 centimeters longer than the height. If the perimeter is 58 centimeters, find the base and the height of the rectangle. Describe/Draw: The shape is a rectangle and we are looking at the perimeter. Investigation 10: a Table to Write Equations from Word Problems Math Notes Defining a Variable When you write an equation, it is important to define the variable carefully. You need to be clear about what you are talking about so that someone else looking at your work understands what the variable represents. This step is an important habit to develop because it is an important step in solving many different math problems.
Checking a Solution To check a solution to an equation, substitute the solution into the equation and verify that it makes the two sides of the equation equal. For example, to verify that x = 10 is a solution to the equation 3(x − 5) = 15, substitute 10 into the equation for x and then verify that the two sides of the equation are equal. As shown at right, x = 10 is a solution to the equation 3(x − 5) = 15. What happens when you do this check if your answer is incorrect? For example, try substituting x = 2 into the same equation. The result shows that x = 2 is not a solution to this equation. Investigation 9: Solving a Word Problem Math Notes Solving Problems with the 5D Process The 5D Process is an organized method to problems. The D’s stand for Describe/Draw, Define, Do, Decide, and Declare. An example of this work is shown below. Problem: The base of a rectangle is 13 centimeters longer than the height. If the perimeter is 58 centimeters, find the base and the height of the rectangle. Describe/Draw: The shape is a rectangle and we are looking at the perimeter. Investigation 10: a Table to Write Equations from Word Problems Math Notes Defining a Variable When you write an equation, it is important to define the variable carefully. You need to be clear about what you are talking about so that someone else looking at your work understands what the variable represents. This step is an important habit to develop because it is an important step in solving many different math problems.
Balancing%20Equations%20Student%20Book.docx