Chapter Prerequisite Skills Chapter Prerequisite Skills Chapter 3 Multi-Step Equations and Inequalities

Chapter Prerequisite Skills 1. Explain what an expression is and what an equation is. Then give one example. Use the distributive property to write and equivalent variable expression. 3. 8( z – 7) 4. -6(- m + 12) An expression can be a variable expression or a numerical expression. It is not equal or compared to anything. 2 x + 7 or 28 – 7 An equation is a mathematical sentence comparing two expressions. 2 x + 7 = 28 – 7 9 x z – 56 6 m – ( x – 4) (n – 5)-10 n + 50

Chapter Prerequisite Skills Solve the equation. Check the solution. 11. h ÷ 6 = q – 9.6 = x + 13 = = -13 b -5 Simplify the Expression b – 12 b ( a + 2) + a 4-3 b a c + 4 – c 9. 2(2 d d )6 d +10

Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 3.1 Solving Two-Step Equations Skill Check Skill Check

Skill Check = ÷ -4 = – 88 = (1 ÷ 765) =1

Writing Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations. Common Words and Phrases that Indicate Operations AdditionSubtractionMultiplicationDivision plus the sum of increased by total more than added to minus the difference of decreased by fewer than less than subtracted from times the product of multiplied by of divided by divided into the quotient of

Study Strategy For example: 3 x + 7 = -5 Subtract 7 from both sides: x + 7 = -5 – 7 Simplify: 3 x = -12 Divide each side by 3: 3 x ÷ 3 = -12 ÷ 3 Simplify: x = -4 When you solve an equation show every step when solving, because these steps are important for diagnosing errors.

Using Subtraction and Division to Solve EXAMPLE 1 SOLUTION a. 8x + 7 = 47 Solve. a. 8x + 7 = x + 7 = x = 5r = -4 b. 1 = 2r + 9c. 2 = 6h + 20 b. 1 = 2r + 9 c. 2 = 6h x = 40 8x/ 8 = 40/ = 2r + 9 – 9 -8 = 2r -8/2 = 2r/2 h = = 6h + 20 – = 6h -18/6 = 6h/6

Using Addition and Multiplication to Solve EXAMPLE 2 SOLUTION a. y/4 – 2 = 1 Solve. a. y/4 – 2 = y/4 – 2 = y = 12d = 15 b. 2 = d/5 - 1c. 12 = f/2 – 8 b. 2 = d/5 - 1 c. 12 = f/2 – 8 y/4 = 3 4(y/4) = (3) = d/5 – = d/5 5(3) = (d/5)5 f = = f/2 – = f/2 2(20) = (f/2)2

Solving an Equation with Negative Coefficients EXAMPLE 3 SOLUTION a. 9 – 6a = 45 Solve. a. 9 – 6a = – 6a = 45 – 9 a = -6m = -1 b. 6 – 2m = 8c. -2 = 5 – n b. 6 – 2m = 8 c. -2 = 5 – n – 6a = 36 – 6a/-6 = 36/ – 2m = 8 – 6 – 2m = 2 – 2m/-2 = 2/-2 n = 7 -5 – 2 = 5 – n – 5 -7 = -n -7/-1 = -n/-1

Writing and Solving a Two-Step Equation EXAMPLE 4 Motorcycle William makes a down payment of 1,100,000 won on a motorcycle costing 2,300,000 won. If no interest is charged, how many monthly payments of 150,000 won must he make until he has finished paying for the motorcycle? Let p represent the number of monthly payments. Write a verbal model. ANSWER SOLUTION William must make 8 monthly payments of won. Amount of down payment + Monthly Payment Number of monthly payments, p = Total Cost of Motorcycle p = p = 8 – p = p = p/ = /150000

Lesson Quiz 1. 9 b + 8 = z /7- 5 = = 20 – 6 c b = 8 z = 14 c = 5 Solve the equation. 5. Challenge Solve (8 + k) /5 = 3 k = – b /6 = 23 b = -72

Closure 2.) Asia girl has lived one fourth of her life in S.Korea, one fifth of her life in Thailand, one third of her life in China, and she has been living in Japan for the past 13 years. How old is Asia girl? 1.) Explain how you solve the equation 11 – 4 p = -1? Asia girl is 60 years old.

Lesson 3.1 Homework: pp Exs. (1, 20, 22, 24, 26, 28, 30, 32, 34, 35abc, 45, 46) Challenge/Bonus 36