Cumulative Standards Review
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Review the new concepts in each section of the chapter and try to relate the mathematical meaning to each of the given terms.
| Term | Mathematical Meaning |
|---|---|
| A. inequality | I |
| B. compound inequality | III |
| C. extraneous solution | II |
| D. expression | Y |
| E. equation | IV |
We are given various mathematical terms. A.inequality B.compound inequality [0.5em] C.extraneous solution D.expression [0.5em] E.equation We will use the given mathematical meanings and decide which term corresponds to each of them.
Recall that >, <, ≥, ≤ are all symbols used to denote a relation where one quantity is different than another one in a specific way. The symbol ≠states that two expressions are not equal. Therefore, the corresponding term is inequality.
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An inequality is a mathematical sentence that contains >,<,≥,≤ or ≠. |
Therefore, term A matches with Meaning I.
When working with absolute value equations, we isolate the absolute value expression and rewrite the original equation into two cases. If the solution of one case does not satisfy the original equation, we say that it is an extraneous solution.
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An extraneous solution is a solution from an equation derived from an original equation but not a solution of the original equation. |
Therefore, term C matches with Meaning II.
We can combine individual inequalities using the word and or the word or. When we do this, the inequalities become one compound inequality.
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A compound inequality is a pair of individual inequalities joined by the word and or the word or. |
Therefore, term B matches with Meaning III.
We use the equals sign to state that two mathematical expressions are equal. This is called an equation.
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An equation is a mathematical sentence that contains an equals sign. |
Therefore, term E matches with Meaning IV.
A mathematical expression is a combination of numbers, operations, and variables. Therefore, the corresponding term is expression.
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An expression is a mathematical phrase that uses numbers, variables, and operational symbols. |
Therefore, term D matches with Meaning V.
We can summarize our answers in a table.
| Term | Mathematical Meaning |
|---|---|
| A. inequality | I |
| B. compound inequality | III |
| C. extraneous solution | II |
| D. expression | Y |
| E. equation | IV |