Overview:
Open sentences in mathematics are sentences that contain variables. They can be true or false depending upon the numbers that are substituted for the variables. Solving open sentences to make them true is an important part of algebra.
What Are Numerical Expressions?
Numerical expressions contain numbers only, such as 4/5, 2 + 4 = 6, 3 X 2 -1, and so forth. These are closed sentences, and are either always true (such as 2 + 4 =6) or always untrue (as 3 +1 =5). They are evaluated by means of arithmetic.
What Are Variables?
Variables are values represented by letters within a number sentence. For example, 3 +y =10 contains the variable y, and l ∙w=a, contains variables l, w, and a. The integer that equals y in the first sentence is 7, but many numbers can be substituted for l and w. Variables are used in algebraic expressions.
What Are Equations?
Equations are number sentences that contain the equals sign, whether or not they contain variables. For example, 2 X 2 = 4 is an equation, as is 14-2 = 12. Sentences such as 2 + x =5 or 3y2 +4 =x are also equations. Sentences do not have to be true to be equations. For example, a sentence like 2 + 2 = 5 is an equation, even though it is false.
What Are Inequalities?
Inequalities are number sentences that contain symbols such as < (less than) or > (greater than). Sentences that contain them can also be open sentences, even though there is more than one value that will make the sentence true. For example, the sentence y > 5 can be solved with an infinite set of numbers. False values for the sentence are also an infinite set of numbers.
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