188 CHAPTER 1 Equations and Inequalities Chapter 1 Test Prep Key Terms New Symbols ∅ empty set i imaginary unit H infinity −H negative infinity 1a, b2 1 −H, a4 s interval notation 3 a, b2 ∣ a ∣ absolute value of a 1.1 equation solution (root) solution set equivalent equations linear equation in one variable first-degree equation identity conditional equation contradiction literal equation simple interest future value (maturity value) 1.2 mathematical model linear model 1.3 imaginary unit complex number real part imaginary part nonreal complex number pure imaginary number standard form complex conjugate 1.4 quadratic equation standard form second-degree equation double solution cubic equation discriminant 1.5 leg hypotenuse 1.6 rational equation proposed solution equation quadratic in form 1.7 inequality linear inequality in one variable interval interval notation endpoint open interval closed interval break-even point quadratic inequality disjoint interval strict inequality nonstrict inequality rational inequality 1.8 absolute value tolerance Quick Review Concepts Examples Solve. 51x + 32 = 3x + 7 5x + 15 = 3x + 7 Distributive property 2x = -8 Subtract 3x. Subtract 15. x = -4 Divide by 2. The solution set is 5-46. 1.1 Linear Equations Addition and Multiplication Properties of Equality Let a, b, and c represent real numbers. If a =b, then a +c =b +c. If a =b and c 30, then ac =bc. How many liters of 30% alcohol solution and 80% alcohol solution must be mixed to obtain 50 L of 50% alcohol solution? Solving an Applied Problem Step 1 Read the problem. 1.2 Applications and Modeling with Linear Equations
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