Section 2.1 Equations and Their Solutions 97 c. Three less than a number is twice the number. Find the number. Write an equation to solve this problem. �������������������������������������� ���������������������������������������������������������������� Three less than a number is expressed as x - 3 and twice a number is 2x. So, the equation is x - 3 = 2x. Let x be the nu number. 3 x x2 - = x Student Check 1 a. equation b. expression c. equation d. expression Student Check 2 a. x = -3 is a solution. b. x = 0 and x = 2 are solutions. Student Check 3 a. 3(n + 5) = 4n b. 2n + 1 = n + 2 Student Check 4 a. a + a - 20 = 180 b. x + x - 288 = 522 ANSWERS TO STUDENT CHECKS SUMMARY OF KEY CONCEPTS 1. An equation is a statement that two expressions are equal. Equations can be solved, whereas expressions can be simplified or evaluated. 2. The number(s) that make an equation a true numerical statement are called solutions of the equation. 3. Expressing statements as mathematical equations takes a lot of practice. It is very important to recognize the key phrases for the different operations and for the equals sign. 4. Writing equations that can be used to solve application problems requires us to know some essential information about the situation. This essential information can be gathered from key words in the problem—perimeter, complementary, supplementary, and the like. GRAPHING CALCULATOR SKILLS The graphing calculator can be used to determine whether a number is a solution of an equation. There are several ways to use the calculator to perform this skill. Example: Determine if x = -2 is a solution of -4x + 2 = 2x - 1. Method 1: Use the calculator to evaluate the left and right sides of the equation. ( ) 4 ( ( ) 2 ) + 2 ENTER 2 ( ( ) 2 ) 2 1 ENTER Since the left side, 10, does not equal the right side, -5, the value x = -2 is not a solution of the equation. Method 2: Enter the left side and right side of the equation in the equation editor and use the table to determine the value of each side. ( ) 4 T u n + 2 ENTER 2 T u n ENTER 2 1 2nd RA H When x = -2, the values in the columns for Y1 and Y2 are not equal. This shows that x = -2 is not a solution.
hendricks_beginning_algebra_1e_ch1_3
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