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Welcome to our Math lesson on Open and Closed Sentences, this is the second lesson of our suite of math lessons covering the topic of Variables, Coefficients and Constants. First Order Equations with One Variable, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
When dealing with algebraic expressions, we considered only terms made by numbers and letters (which may also contain indices) connected through basic arithmetic operations such as addition and subtraction. Such expressions are known as 'open sentences', as every algebraic expression is nothing more than a word sentence written in a shorter way using mathematical symbols. They are called 'open' because no further information is provided to confirm if the sentence is true or false.
For example, 2x - 1; x2 + 5y - 4z; 1/y2, etc., are examples of open sentences (algebraic expressions) as their value is unknown until we provide further information.
However, if the value of the expression is provided (it must be written in the same row after the 'equal to' sign), it is no longer an algebraic expression but an equation instead. For example,
are examples of equations, as the value of the corresponding sentences is known. Therefore, equations are examples of 'close sentences', i.e. sentences that we know are true because there is a value to the right of the 'equal' symbol.
By definition, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions (open sentences) that have the same value. When combined, these two equal open sentences form a single closed sentence.
The difference between closed sentences and equations is that closed sentences may be either true or false while equations are supposed to be always true.
Identify the open sentences that form the following equations:
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