![]() ![]() ![]() For instance, in the exponential equation of 73 = 147, the exponent of 3 tells you to multiply seven with itself repeatedly, so 73 = 7 x 7 x 7 = 147. Exponents operate by multiplying their coefficients repeatedly the number of times the exponent represents. Exponential equationsĮxponential equations contain numerical terms and exponents and sometimes include variables, depending on the type of problem you're solving. Linear equations can also be as simple as an arithmetic problem like 3 + 4 = 7, or they can be more complex, like solving equations of lines, as in 3x + y = 12. Additionally, as mathematics becomes more complex, such as trigonometry and calculus, linear equations can combine to form quadratic and trigonometric functions. Linear equations can explain the path of geometric lines and segments and represent a primary step in algebra. Linear equations are the most common simple equation and typically consist of one or several terms on either side of an equal sign. However, most simple equations fall into several categories: Linear equations The types of mathematical equations you can encounter range from simple to more complex problems. Related: Basic Math Skills: Definition, Examples and How To Improve Them Types of simple equations In this case, the variable represents an unknown value that results in a sum of 10 when you add it to five. You may also have a mix of numerical and variable terms within a simple equation, such as in the equation 5 + a = 10. Another example of a simple equation is 5 + 11 - 2 = 14, where you see multiple terms that split between two operation signs and the equal sign. However, in most simple equations, you calculate a problem containing one or a few numerical terms.įor example, the equation 3 x 4 = 12 contains single terms that the operation and equal signs separate. As mathematics becomes more complex in level, simple equations can become larger with additional terms and variables. Simple equations also follow one or a combination of the four mathematical operations of addition, subtraction, multiplication and division. There is no value that will ever satisfy this type of equation.A simple equation represents a relationship between two terms on either side of an equal sign. This type of equation is never true, no matter what we replace the variable with. The last type of equation is known as a contradiction, which is also known as a No Solution Equation. For this type of equation, the solution is all real numbers. No matter what value we replace x with, the equation is true. If we simplified each side we would get: 3x - 15 = 3x - 15. The left and the right side can be simplified to match each other. The second equation, an identity is always true, no matter what value replaces the variable. This equation is true when x = 4, but false when x is any other value. As an example, suppose we look at 3x = 12. The first type of equation, known as a conditional equation is true under certain conditions, but false under others. These are conditional equations, identities, and contradictions. When solving equations, we will encounter three types of equations. When we encounter special case equations, we will see No Solution Equations and Equations that have infinitely many solutions. ![]() In this section, we learn about special case linear equations.
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