clear definition of important terms for substution and and example problem?
http://www.freemathhelp.com/substitution.html
http://www.icoachmath.com/math_dictionary/Substitution_Method.html
Certainly! The terms you mentioned, "substitution" and "example problem," are commonly used in mathematics. Let's start by defining each term:
1. Substitution: In mathematics, substitution refers to the process of replacing a variable in an equation or expression with a specific value. This allows us to simplify and evaluate the expression or equation. Substitution is commonly used to solve equations and evaluate functions.
2. Example problem: An example problem serves as a demonstration or illustration of how to apply a concept or solve a particular type of mathematical problem. It helps in understanding the steps and methods involved in finding a solution.
To provide a clear understanding, let's go through an example problem involving substitution:
Example problem: Solve the equation 3x - 7 = 13 by using substitution.
Solution:
Step 1: Start with the given equation: 3x - 7 = 13
Step 2: Solve for x by isolating the variable. In this case, we need to get rid of the constant term (-7) on the left side of the equation. To do this, we can add 7 to both sides:
3x - 7 + 7 = 13 + 7
Simplifying the equation gives us:
3x = 20
Step 3: Now that we have an equation with only one variable, we can use substitution. Choose a value to substitute for x. Let's pick x = 6 as an example:
3(6) = 20
Simplifying further:
18 = 20
Step 4: Since 18 is not equal to 20, we realize that our initial substitution (x = 6) was incorrect. Let's try another value. For instance, let's substitute x with 9:
3(9) = 20
Simplifying:
27 = 20
Step 5: We can clearly see that 27 is not equal to 20. This means that our second substitution (x = 9) was incorrect as well. Therefore, we conclude that there is no solution to the equation 3x - 7 = 13.
In this example, we used the concept of substitution to test different values for x and determine if any of them satisfy the given equation. By substituting values, we attempted to find a solution to the problem.