Open Sentences in Algebra
Yes, sentences are not only used in English class, but also in Math! In algebra a sentence contains numbers, variables, operations and either an equal sign (=) or an inequality symbol.
A sentence that contains an equal sign (=) is called an equation. If a sentence is not an equation, then it is an inequality. Take a look at the following mathematical symbols for their corresponding meanings:
An open sentence is a sentence that contains one or more variables that may be true or false depending on what values you substitute for the variables. For example:
As you discovered in the example above, the equations (open sentences with an equal sign) that we will study in this unit (linear equations) only have one solution, or one value for the variable that will make the sentence true.
Let's take a look at how you might find a solution for a sentence that is an equation (with an equal sign).
Ok, so that's not too hard. You need to have great mental math skills to find the solution to open sentences.
A sentence that is an inequality, may have many values for the variable that make the sentence true. Take a look:
As you can see, there are many solutions when working with inequalities. We can express all of these solutions by using the inequality symbol in our answer.
Let's take another look at how you might find a solution for an open sentence that is an inequality.
If your mental math skills are not up to par, then you may have trouble finding solutions for these math sentences. When you use integers in math sentences, then finding the solutions can be really tough. Therefore, our next set of lessons will focus on methods that are used to solve equations.
We will start with a lesson on solving addition equations.
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