94 Chapter 2 Linear Equations and Inequalities in One Variable Student Check 2 Determine if the given numbers are solutions of the equation. a. 1 - 2x=-5x - 8; x=-3, 1 4 , or 2 b. x2 = 2x; x = 1 2 , 0, or 2 Translating Phrases into Mathematical Equations In Chapter 1, we learned how to translate phrases into mathematical expressions and equations. The phrases for equality are shown in the following table. Phrases for “ = ” is equal to the result is is the same as equals is In many sections of this book, we will be required to solve application problems. The most difficult part of solving an application problem is setting up the equation correctly. Example 3 illustrates the process of setting up an equation to solve an application problem. We will only set up the equation. Solving the equations will come later. ���������������������� Expressing Statements as Mathematical Equations Step 1: Read the problem carefully. Step 2: Determine the unknown and assign a variable to it. (If there is more than one unknown, the other unknowns will be represented in terms of the same variable initially chosen.) Step 3: From the given statement, determine the phrase that represents the equals sign. The expression before this phrase is the left side of the equation. The expression after the phrase is the right side of the equation. Translate both expressions and set them equal to obtain the equation. �� ������������������������ ������������������ For each problem, define a variable and write an equation that can be used to solve the problem. 3a. Twice the sum of a number and 3 is the same as 4 less than the number. Solution 3a. What is unknown? The number is unknown. Let n represent the number. What is known? Twice the sum of a number and 3 is the same as 4 less than the number. The phrase “is the same as” represents the equals sign. “Twice the sum of a number and 3” represents the left side of the equation. “Four less than the number” represents the right side of the equation. Twice the sum of a number and 3 is the same as 4 less than the number 2(n + 3) = n - 4 So, the equation used to solve this problem is 2(n + 3) = n - 4. 3b. The difference of three times a number and 6 is the same as the quotient of the number and 9. Objective 3 ▶ Express statements as mathematical equations.
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