122 Chapter 2 Linear Equations and Inequalities The addition and subtraction properties of equality indicate that adding or subtracting the same quantity on each side of an equation results in an equivalent equation. This means that if two equal quantities are increased or decreased by the same amount, then the resulting quantities will also be equal (Figure 2-1). 20 lb 50 lb 20 lb 50 lb 50 50 lb lb Figure 2-1 Applying the Addition and Subtraction Properties of Equality 50 50 50 20 50 20 Example 2 Solve the equations. a. p 4 11 b. w 5 2 Solution: In each equation, the goal is to isolate the variable on one side of the equation. To accomplish this, we use the fact that the sum of a number and its opposite is zero and the difference of a number and itself is zero. a. p 4 11 p 4 4 11 4 14 4 02. To isolate p, add 4 to both sides Simplify. Check by substituting into the original equation. Check: p 0 15 p 15 p 15 p 4 11 15 4 11 The solution is 15. ✔ True b. 11 11 To isolate w, subtract 5 from both sides 15 5 02. Simplify. Check by substituting into the original equation. Check: w 5 2 w 5 5 2 5 w 0 7 w 7 w 7 w 5 2 7 5 2 The solution is 7. 2 2 ✔ True Classroom Examples: p. 129, Exercises 16 and 18 Answers 7. 9 8. 0 70 70 Skill Practice Solve the equations. 7. v 7 2 8. x 4 4 Instructor Note: You may want to mention that sometimes a solution to an equation is expressed as a solution set.
miller_introductory_algebra_3e_ch1_3
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