Identifying Types of Equations

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In this section, we learn about special case linear equations. When we encounter special case equations, we will see No Solution Equations and Equations that have infinitely many solutions. When solving equations, we will encounter three types of equations. 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, which is also known as a No Solution Equation. 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.
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