1. Objectives: Solve equations by multiplying and dividing Write an equation that expresses a problem solving situation Section 2-1 Solve one-step Equations SPI 11B: identify the opposite of a rational number SPI 21E: Solve one and two step linear equations Reciprocal or Multiplicative Inverse Any number multiplied by its inverse is equal to 1. INVERSE

2. Reciprocal of a Number 1 5 NAME THE RECIPROCAL OF: 5 1 5 = Term Reciprocal 3 2 2 3 x 3 = 1 3 x 3 1 x=3x 2x 7 = 2 7 x 7 2 x

3. Properties of Equality – Used to Solve Equations Multiplication Property of Equality: For every real number a, b, and c if a = b, then a ∙ c = b ∙ c. 6 = 3 6 ∙ 2 = 3 ∙ 2 2

4. Solve – = –9.3 t 6 t=55.8Simplify. – 6 (– )=– 6(9.3)Multiply by –6 on each side to get the variable alone on the left side of the equal sign. t6t6 Solve a One-step Linear Equation using Reciprocal Solve y = –10 2525 y=–25Simplify. ( )y= (–10)Multiply each side by, the reciprocal of. 2525 5252 5252 5252 2525 Check:y=–10 2525 (–25)–10Substitute –25 for y. 2525 –10=–10

5. Properties of Equality – Used to Solve Equations Division Property of Equality: For every real number a, b, and c if a = b, then a = b c c 3 + 1 = 4 2 2

6. Solve –6m = 42. m=–7Simplify. =Divide each side by –6. –6m –6 42 –6 Solve a One-step Linear Equation by Dividing Solve 3m = 45. m=15Simplify. =Divide each side by 3. 3m 3 45 3

7. Solve each equation: 1.4c = -96 2. 3a = 12 3. -1/4m = 8 4. 3/4x = 9 4c = -96 4 4 c = -24 (- 4/1)(-1/4m) = (-4/1)(8) m= -32- (4/3)(3/4x) = (4/3)(9) x = 36/3 = 12 3a = 12 3 3 a = 4 Practice Solving

8. Writing and Solving Equations When writing equations focus on certain words that can be translated to an algebraic symbol. a number (means a variable) is (means equal =) less than, subtract, decrease (subtract - ) sum, increase (add +) product, times (multiply) quotient, divided by (divide)