Section 2.1 Solving Linear Equations 55 Solutions 2a. 12.5 = d - 2.5 Objective 3 ▶ Use the multiplication property of equality. 12.5 + 2.5 = d - 2.5 + 2.5 Add 2.5 to each side. 15 = d Simplify. Check: 12.5 = d - 2.5 Begin with the original equation. 12.5 = 15 - 2.5 Replace d with 15. 12.5 = 12.5 Simplify. The value 15 makes the equation true, so the solution set is 5156. 2b. We must isolate the variable terms on one side of the equation and the constant terms on the other side. 12 + 2g = 3g + 15.4 12 + 2g - 2g = 3g - 2g + 15.4 Subtract 2g from each side. 12 = g + 15.4 Simplify. 12 - 15.4 = g + 15.4 - 15.4 Subtract 15.4 from each side. -3.4 = g Simplify. Check: 12 + 2g = 3g + 15.4 Begin with the original equation. 12 + 2(-3.4) = 3(-3.4) + 15.4 Replace g with -3.4. 12 - 6.8 = -10.2 + 15.4 Simplify each side. 5.2 = 5.2 Simplify. The value -3.4 makes the equation true, so the solution set is 5-3.46. Student Check 2 Use the addition property of equality to solve each linear equation and check the solution. a. 4.3 = f + 9.1 b. 2 + 6y=-10 + 5y The Multiplication Property of Equality The addition property of equality can be used to eliminate a value that is added to or subtracted from a variable term. To eliminate a value that multiplies or divides a variable term, we must use the multiplication property of equality. Property: Multiplication Property of Equality For a, b, and c(c ≠ 0) real numbers, a = b is equivalent to ac = bc So, when two equal quantities are multiplied by the same nonzero number, the resulting expressions are equal. Because division is defined in terms of multiplication, we can also divide each side of an equation by the same nonzero number and obtain an equivalent equation.
hendricks_intermediate_algebra_1e_ch1_3
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