2. ALGEBRA READINESS LESSON 3-4 Warm Up Lesson 3-4 Warm Up

3. ALGEBRA READINESS LESSON 3-4 Warm Up Lesson 3-4 Warm Up

4. ALGEBRA READINESS “Solving Two-Step Equations” (3-4) What is a two-step equation? How can you use a model to show how to solve a two-step equation? Two-Step Equation: an equation that involves “undoing” two operations In the following model, represents -1, represents 1, and represents a variable, like x. This means that equals 0 (in other words, they “cancel each other out”), since 1 – 1 = 0. cancel out (“zero pair”) x -x 1 1 1 1 1 1 1 1 xx 1 1

5. ALGEBRA READINESS “Solving Two-Step Equations” (3-4) How do you solve equations involving more than one step. To solve equations, use the addition, subtraction, multiplication, and division properties of equality which say that the equation stays equal, or balanced, if you add, subtract, multiply, or divide both sides by the same number. Simply use the properties of equality repeatedly to get the variable alone on one side of the equation with a coefficient of 1 (Examples: 1x, 1t, 1c)

6. ALGEBRA READINESS Solve –y + 7 = –12. –y + 7 = –12 Subtraction Property of Equality - 7 - 7 –y = –19 Simplify. (–1)(–y) = (–1)(–19) Multiplication Property of Equality y = 19 Simplify. Check: –y + 7 = –12 –(19) + 7 –12 Substitute 19 for y. –12 = –12 Solving Two-Step Equations LESSON 3-4 Additional Examples

7. ALGEBRA READINESS Solve 2.25 + = 8.5. h5h5 = 6.25 Simplify. h5h5 2.25 + = 8.5 h5h5 – 2.25 h5h5 Subtraction Property of Equality h = 31.25 Simplify. = 6.25 5 Multiplication Property of Equality h5h5 Solving Two-Step Equations LESSON 3-4 Additional Examples 4 10 5151 1 1 0 + 0 1

8. ALGEBRA READINESS The Science Club sells birdfeeders for $8 each. The club spends $32 in building materials. The club’s profit is $128. How many birdfeeders did the club sell? The club sold 20 birdfeeders. 8b – 32 = 128 Addition Property of Equality + 32 + 32 8b = 160 Simplify. 8b88b8 160 8 = Division Property of Equality Use a model to help write an equation. b = 20 Simplify. 8b – 32 = 128 Write the equation. Solving Two-Step Equations LESSON 3-4 Additional Examples 1 1 + 0 1

9. ALGEBRA READINESS Solve 13 = + 5. 24 = y Simplify. y3y3 13= + 5Subtract 5 from each side. - 5 y3y3 8 = Simplify. y3y3 3 8 = Multiply each side by 3. y3y3 13 = 13 13 8 + 5 (24) 3 13 + 5 Substitute 24 for y. y3y3 Check: 13 = + 5 Solving Two-Step Equations LESSON 3-4 Additional Examples 3131 1 1 + 0 1

10. ALGEBRA READINESS You order iris bulbs from a catalog. Iris bulbs cost $0.90 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 = 18.50 Subtract 2.50 from each side. – 2.50 – 2.50 0.90b = 16.00Simplify. Words: cost times number of plus shipping equals amount per iris iris bulbs to spend Define: Let b = the number of bulbs you can order. Equation: 0.90 b + 2.50 = 18.50 Solving Two-Step Equations LESSON 3-4 Additional Examples + 0

11. ALGEBRA READINESS You can order 17 bulbs. 0.90b 0.90 = 16 0.90 Divide each side by 0.90. 1b = 17.7 Simplify. (continued) 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. Solving Two-Step Equations LESSON 3-4 Additional Examples 1 1

12. ALGEBRA READINESS Solve each equation. 1.6a + 12 = 302. + 21 = 24 3.4c – 40 = 284. + 15 = 22 b5b5 d7d7 315 17 49 Solving Two-Step Equations LESSON 3-4 Lesson Quiz