Solving Linear Equations and Inequalities Chapter 2.

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Presentation transcript:

Solving Linear Equations and Inequalities Chapter 2

Angel, Elementary Algebra, 7ed – Combining Like Terms 2.2 – The Addition Property of Equality 2.3 – The Multiplication Property of Equality 2.4 – Solving Linear Equations with a Variable on One Side of the Equation 2.5 – Solving Linear Equations with a Variable on Both Sides of the Equation 2.6 – Formulas 2.7 – Ratios and Proportions 2.8 – Inequalities in One Variable Chapter Sections

Angel, Elementary Algebra, 7ed 3 Adding with Same Signs To add real numbers with the same sign, add their absolute values. The sum has the same sign as the numbers being added. Example: –12 + (–3) = – = 34 The sum of two positive numbers will always be positive and the sum of two negative numbers will always be negative.

Angel, Elementary Algebra, 7ed 4 Adding with Different Signs To add real numbers with the different signs, subtract the smaller absolute value from the larger absolute value. The sum has the sign of the number with the larger absolute value. Example: 12 + (–3) = 9– = 4 The sum of two numbers with different signs may be positive or negative. The sign of the sum will be the same as the sign of the number with the larger absolute value.

§ 2.1 Combining Like Terms

Angel, Elementary Algebra, 7ed 6 The parts in an algebraic expression that are added are called the terms of the expression. Expression -3x + 8y w z - Terms -3x, 8y, -15 6w 2, 12z, - Terms

Angel, Elementary Algebra, 7ed 7 The numerical part of a term is the numerical coefficient or coefficient. Coefficient -3 8, since means x 6 Term -3x 8y 6w 2 Terms

Angel, Elementary Algebra, 7ed 8 Like terms are terms that have the same variables with the same exponents. Like Terms -3x, 8x, - x 6w 2, -12w 2, w 2 Unlike Terms 20x, x 2, x 3 6xy, 2xyz, w 2 Like Terms

Angel, Elementary Algebra, 7ed 9 Combining Like Terms 1.Determine which terms are like terms. 2.Add or subtract the coefficients of the like terms. 3.Multiply the number found in step 2 by the common variable(s). Example: 5a + 7a = 12a

Angel, Elementary Algebra, 7ed 10 Distributive Property For any real numbers a, b, and c, a(b + c) = ab + bc Example: 3(x + 5) = 3x + 15 (This is not equal to 18x! These are not like terms.)

Angel, Elementary Algebra, 7ed 11 Simplifying an Expression 1.Use the distributive property to remove any parentheses. 2.Combine like terms. Example: Simplify 3(x + y) + 2y = 3x + 3y + 2y (Distributive Property) = 3x + 5y(Combine Like Terms) (Remember that 3x + 5y cannot be combined because they are not like terms.)