6.1 Order of Operations and Solving Linear Equations 299 In Example 4, we showed the step + = x 0 20. This step is usually done mentally, and the step is usually not listed. Subtraction Property of Equality If = a b, then − = − a c b c for all real numbers a b , , and c. Learning Catalytics Keyword: Angel-SOM-6.1 (See Preface for additional details.) The subtraction property of equality indicates that the same number can be subtracted from both sides of an equation without changing the solution. Example 5 Using the Subtraction Property of Equality Determine the solution to the equation + = x 17 19. Solution To isolate the variable, subtract 17 from both sides of the equation. x x x 17 9 17 17 9 17 8 + = + − = − = − 7 Now try Exercise 47 Note in Example 5 that we did not subtract 9 from both sides of the equation, because doing so would not result in getting x by itself on one side of the equation. Now we discuss the multiplication property. Multiplication Property of Equality If = a b, then ⋅ = ⋅ a c b c for all real numbers a b , , and c, where ≠ c 0. The multiplication property of equality indicates that both sides of the equation can be multiplied by the same nonzero number without changing the solution. Example 6 Using the Multiplication Property of Equality Determine the solution to = x 4 8. Solution To solve this equation, we isolate the variable by multiplying both sides of the equation by 4. = ⎛ ⎝ ⎞ ⎠ = = = = x x x x x 4 8 4 4 4(8) 4 4 32 1 32 32 1 1 7 Now try Exercise 49 In Example 6, we showed the steps = x4 4 32 and = x1 32. Usually, we will not illustrate these steps.
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