Section 2.4 More on Solving Linear Equations 133 Solution: Method 1: Enter each side of the equation in the equation editor and view the table. Since the calculator accepts only the variable x, we will use x in place of y in the equation. Instead of scrolling to x = 51 in the table, we can change the starting value of the table. 2nd N 5 ENTER 2nd RA H When we view the table we see the x-value of 51 and find that the corresponding y-values are equal, which confirms x = 51 is a solution of the equation. Method 2: We can also change the table settings to enable us to enter the value of x that we want to check. Go to the Table Setup and change the Indpnt setting from Auto to Ask. Move the cursor to Ask in the Indpnt row and press enter. 2nd N Now go to the table and enter the value for x and press enter. 5 1 RA H ENTER 2nd Since the y1 and y2 values are equal for x = 51, the solution is correct. ������������ If the equation is an identity, the Y1 and Y2 values are equal for every value of x. If the equation is a contradiction, the Y1 and Y2 values are not equal for any value of x. �� ���������������� �������� EXERCISE SET 9. If the solution of the equation x + a = x + b is the empty set, then a ≠ b. 10. If the solution of the equation x + a = x + b is all real numbers, then a = b. 11. An equivalent form of the equation y 4 + 3 = y 8 is 2y + 3 = y. 12. An equivalent form of the equation -5(2x - 3) = 2x - 9 is -10x - 3 = 2x - 9. Practice Makes Perfect! Solve each equation by fi rst clearing fractions. (See Objective 1.) 13. x 2 + 3 2 = 1 2 14. y 3 - 4 3 =- 10 3 15. a 6 + 5 = a 3 16. x 5 - 2 = x 10 Write About It! Use complete sentences to explain the meaning of the given term. 1. Conditional equation 2. Contradiction 3. Identity Use complete sentences to answer each question. 4. How can you eliminate fractions from an equation? 5. How can you eliminate decimals from an equation? 6. When solving an equation, how will you know if the solution is the empty set? 7. When solving an equation, how will you know if the solution is all real numbers? Determine if each statement is true or false. If a statement is false, explain why. 8. The solution of the equation 2x = 5x is the empty set.
hendricks_beginning_algebra_1e_ch1_3
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