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hendricks_beginning_algebra_1e_ch1_3

104 Chapter 2 Linear Equations and Inequalities in One Variable Check: b + 1 2 =- 3 2 Original equation -2 + 1 2 =- 3 2 Replace b with -2. - 4 2 + 1 2 =- 3 2 Write -2 with the LCD of 2 and simplify. - 3 2 =- 3 2 Simplify. Since b = -2 makes the equation true, the solution set is {-2}. 2d. Since the variable r is on the right side, we will isolate the variable on the right side by subtracting 2.1 from each side. 1.8 = 2.1 + r 1.8 - 2.1 = 2.1 + r - 2.1 Subtract 2.1 from each side. -0.3 = r Simplify each side of the equation. r=-0.3 While the equation is solved when r is isolated on the right side, note that we can write the final answer with the variable on the left since a = b is equivalent to b = a. Check: 1.8 = 2.1 + r Original equation 1.8 = 2.1 + (-0.3) Replace r with -0.3. 1.8 = 1.8 Simplify. Since r = -0.3 makes the equation true, the solution set is {-0.3}. Student Check 2 Solve each equation using the addition property of equality. Check each answer. a. y - 5=-2 b. y + 10=-9 c. x - 1 3 = 5 3 d. 4 = 2.4 + x Multistep Equations The equations we solved in Example 2 were set up to immediately apply the addition property of equality since each side of the equation was as simplified as possible and because each equation contained a single variable term. This is not the case for most equations. Most equations require us to do some work to get them in the form that enables us to apply the addition property of equality. ���������������������� Using the Addition Property of Equality Step 1: Simplify each side as much as possible by combining any like terms, removing parentheses, and the like. Remember that each side must be treated as a separate expression. Step 2: If there are variable terms on both sides of the equation, use the addition property of equality to remove the variable term from one side of the equation. Step 3: If there is a term still attached to the variable, use the addition property of equality to isolate the variable. Step 4: Simplify each side of the equation. The equation should be in the form “x = some number” or “some number = x.” Step 5: Check the solution by substituting the value into the original equation. Step 6: Write the solution set in set notation. Objective 3 ▶ Solve equations that require more than one step.


hendricks_beginning_algebra_1e_ch1_3
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