In this Section:
In this section, we learn about the three types of equations that we will encounter. These are conditional equations, identities, and contradictions. The first type of equation, known as a conditional equation is true under certain conditions, but false under others. As an example, suppose we look at 3x = 12. This equation is true when x = 4, but false when x is any other value. The second equation, an identity is always true, no matter what value replaces the variable. The left and the right side can be simplified to match each other. As an example, 3(x - 5) = 3x - 15. If we simplified each side we would get: 3x - 15 = 3x - 15. No matter what value we replace x with, the equation is true. For this type of equation, the solution is all real numbers. The last type of equation is known as a contradiction. This type of equation is never true, no matter what we replace the variable with. As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation.