College Algebra (Abridged)

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( −∞ , 2) ( −∞ , 1] [ − 3, ∞ )

1.3 Mathematical Translations of Equalities fromWords An equation is used to show that two mathematical expressions are equal to each other. For instance, 2 + 5 = 9 . This is as an equation since the expressions on both sides of the sentence are equal and denoted by the equal to (=) sign. Some of the examples of equations are:

3 + 5 = 8 5 – 10 = 10 2 ∗ 3 = 8– 2 70 = 280

In these examples, the expressions on either side of the equal sign are equal to each other. Written sentences can be converted into mathematical expressions so that they can be solved to arrive at meaningful solutions. For instance, “a number is multiplied by 10 and then added to 8 to get 48”. Assume the number is and the mathematical equation becomes: 10 + 8 = 48 It should be noted that the two sides of the equation should balance each other using the equal to (=) sign. Let us solve a few more examples to get a better understanding. Word Problem Algebraic Translation Kathy asks her mother how old she is. Her mother replies, “If you double my age and add 10 to it, then divide by 2, you get 35.” (2 + 10) 2 = 35

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