1. Objectives: Solve Two-Step linear equations Model the steps for solving linear equations Write an equation that symbolically expresses a problem solving situation. Section 2-2 Solve two-step Equations SPI 11B: identify the opposite of a rational number SPI 21E: Solve one and two step linear equations

2. Solve a Two-step Linear Equation 3x - 2 = 4 1. Circle all terms with a variable: 3x - 2 = 4 2. Do all addition and subtraction first: 3x - 2 = 4 +2 +2 Add 2 to both sides 3x = 6 Simplify 3. Write your new equation. 3x = 6 4. Solve using Multiplication or Division. 3x = 6 3 3 Divide each side by 3 x = 2 Simplify

3. Solve 13 = + 5. y3y3 24 = y Simplify. 13 – 5 = + 5 – 5Subtract 5 from each side. y3y3 8 = Simplify. Write your new equation. y3y3 3 8 = 3 Multiply each side by 3. y3y3 Check: 13 = + 5 y3y3 13 + 5Substitute 24 for y. 24 3 13 8 + 5 13 = 13 Add or subtract first then multiply or divide Practice: Solve a two-step Linear Equation Circle the term with the variable and then leave it alone until the end.

4. Solve 21 = –p + 8 21 – 8=–p + 8 – 8Subtract 8 from each side. 13=–pSimplify. Write your new equation 13=- p Use the Division Property -1 -1of Equality. Divide each side by –1. –13=pSimplify. Check: 21=–p + 8 21–(–13) + 8Substitute –13 for p. 21=21Simplify. Solve by multiplying by -1 Practice: Solve a two-step Linear Equation Circle the term with the variable and then leave it alone until the end.

5. Solve the equation s = d for d. t Physical Science Meets Algebra Circle the term you want to solve for. s = d t Use the multiplication property of equality to solve for d. t ∙ s = d ∙ t t t ∙ s = d ∙ t t Simplify the equation. Rewrite the equation. ts = d How does the equation relate to physical science?

6. Solve 8 = – + 4. Justify each step. –96=cSimplify. c 24 8 – 4=– + 4 – 4Subtraction Property of Equality c 24 4=–Simplify. c 24 –24(4)=(–24)(– )Multiplication Property of Equality c 24 3 – 5z – 3=18 – 3Subtraction Property of Equality –5z=15Simplify. z=–3Simplify. Solve 3 – 5z = 18. Justify each step. Check: 3 – 5(-3) = 18 3 + 15 = 18

7. Geometry Meets Algebra In the triangle, the measure of = the measure of Find the value of x. Step 1: Write an equation to show the relationship between the two angles. 4x + 1 = 63 Step 2: Solve the equation for x. 4x + 1 = 63 original equation 4x + 1 – 1 = 63 – 1 SPE 4x = 62 Simplify x = 15.5DPE

8. You order iris bulbs from a book. Iris bulbs cost $.90 each. The shipping charge is $2.50. If you have $18.50 to spend, how many iris bulbs can you order? 0.90b + 2.50 = 18.50 0.90b + 2.50 – 2.50 = 18.50 – 2.50 0.90b = 16 You can order 17 bulbs. b = 17.7 0.90b 0.90 = 16 0.90 Check: Is the solution reasonable? You can only order whole iris bulbs. Since 18 bulbs would cost 18 0.90 = 16.20 plus $2.50 for shipping, which is more than $18.50, you can only order 17 bulbs. Real World Problem for using Two-Step Equations Step 1. Define the variable (unknown) b = number of bulbs Step 2. Write Equation to relate cost of bulbs.90b + 2.50 = 18.50 Step 3. Solve Equation

9. Modeling - Solving Two-step Equations 1. The tiles model the equation 3x – 2 = 4 2. Add 2 tiles to each side (Addition Property of Equality) 3. Remove zero pairs and divide into 3 equal groups 3x – 2 + 2 = 4 + 2 3x = 6 3 3 4. Each green tile equals two yellow tiles so … x = 2