An equation is an algebraic statement that two expressions are equal. An equation consists of:
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Solutions and Solution Sets We will start off this chapter with a fairly short section with some basic terminology that we use on a fairly regular basis in solving equations and inequalities.
So, just what do we mean by satisfy? Example 1 Show that each of the following numbers are solutions to the given equation or inequality. First plug the value into the equation. In this case we will say that a number will satisfy the inequality if, after plugging it in, we get a true inequality as a result.
For equations that will mean that the right side of the equation will not equal the left side of the equation. Now, there is no reason to think that a given equation or inequality will only have a single solution.
We call the complete set of all solutions the solution set for the equation or inequality. Regardless of that fact we should still acknowledge it. For the two equations we looked at above here are the solution sets. Depending on the complexity of the inequality the solution set may be a single number or it may be a range of numbers.
If it is a single number then we use the same notation as we used for equations. If the solution set is a range of numbers, as the one we looked at above is, we will use something called set builder notation. Here is the solution set for the inequality we looked at above.
Consider the following equation and inequality. In other words, there is no real solution to this equation. For the same basic reason there is no solution to the inequality.
We need a way to denote the fact that there are no solutions here. In solution set notation we say that the solution set is empty and denote it with the symbol: This symbol is often called the empty set.
We now need to make a couple of final comments before leaving this section. In the above discussion of empty sets we assumed that we were only looking for real solutions. It is a nice notation and does have some use on occasion especially for complicated solutions.
Therefore, that is what we will not be using the notation for our solution sets. However, you should be aware of the notation and know what it means.Search the world's information, including webpages, images, videos and more. Google has many special features to help you find exactly what you're looking for.
definition of absolute value is used in solving these equations. For any real numbers plus or minus 20 square inches. Write and solve an absolute value equation to determine the least and greatest possible sizes for the head of an adult tennis racket.
= -4 is never true. Thus, it has no solution. The solution set for this type of. This is a tutorial on solving equations with absolute value. Detailed solutions and explanations are included. Detailed solutions and explanations are included.
Example 1: Solve the equation.
Section Solving Absolute Value Equations 31 Identifying Special Solutions When you solve an absolute value equation, it is possible for a solution to be srmvision.com extraneous solution is an apparent solution that must be rejected because it does not satisfy the original equation.
This equation has no solution. Solving Absolute Value Equations of the Type | x | = | y |. If the absolute values of two expressions are equal, then either the two expressions are equal, or they are opposites.
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