* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Solving Two-Step Equations
Survey
Document related concepts
Schrödinger equation wikipedia , lookup
BKL singularity wikipedia , lookup
Calculus of variations wikipedia , lookup
Maxwell's equations wikipedia , lookup
Itô diffusion wikipedia , lookup
Equation of state wikipedia , lookup
Euler equations (fluid dynamics) wikipedia , lookup
Navier–Stokes equations wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Schwarzschild geodesics wikipedia , lookup
Equations of motion wikipedia , lookup
Differential equation wikipedia , lookup
Transcript
Lesson 3-4 Warm-Up 1. 4. 2. 5. 3. 6. 7. ALGEBRA READINESS Solving Multi-Step Equations If a equals “1”, what is a equal to so that both sides of the scale are balanced? 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 . 11. 13. 14. 12. 15. ALGEBRA READINESS LESSON 3-4 Warm Up Lesson 3-4 Warm Up ALGEBRA READINESS LESSON 3-4 Warm Up Lesson 3-4 Warm Up ALGEBRA READINESS “Solving Two-Step Equations” (3-4) What is a two-step equation? Two-Step Equation: an equation that involves “undoing” two operations How can you use a model to show how to solve a two-step equation? 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. 1 cancel out (“zero pair”) 1 x x x -x 1 1 1 1 1 -1 1 1 1 ALGEBRA READINESS “Solving Two-Step Equations” (3-4) To solve equations, use the addition, subtraction, multiplication, and How do you solve equations involving more division properties of equality which say that the equation stays equal, or balanced, if you add, subtract, multiply, or divide both sides by the than one step. 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) ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Additional Examples Solve –y + 7 = –12. –y + 7 -7 –y + 0 = –12 - 7 = –19 Subtraction Property of Equality Simplify (Identity Property of Addition) –1y __ -1 = –19 ___ -1 Identity Property of Multiplication y = 19 Simplify. Check: –y + 7 = –12 –(19) + 7 –12 Substitute 19 for y. –12 = –12 ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Additional Examples Solve 2.25 + 2.25 + h 2.25 + 5 h = 8.5. 5 h = 8.5 5 4 10 = 8.5 0 – 2.25 – 2.25 h 0 + 5 = 6.25 Subtraction Property of Equality Simplify. 1 5 1h • = 6.25 • 5 5 1 Multiplication Property of Equality 1 1h = 31.25 Simplify. ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Additional Examples 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? Use a model to help write an equation. 8b – 32 = 128 Write the equation. 8b – 32 = 128 + 32 + 32 8b + 0 = 160 Addition Property of Equality Simplify. 1 8b 160 = 8 8 Division Property of Equality 1 b = 20 Simplify. 1 The club sold 20 birdfeeders. ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Additional Examples Solve 13 = 13 = y +5 3 -5 8= -5 y +0 3 1 3•8= 3 • y 3 1 24 = 1 y Check: 13 = 13 13 1 y +5 3 (24) +5 3 y + 5. 3 Subtract 5 from each side. Simplify. Multiply each side by 3. Simplify. Substitute 24 for y. 8 +5 13 = 13 ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Additional Examples 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? Words: cost times number of per iris iris bulbs plus shipping equals amount to spend Define: Let b = the number of bulbs you can order. Equation: 0.90 • b + 2.50 = 18.50 0.90b + 2.50 = 18.50 0.90b + 2.50 = 18.50 Subtract 2.50 from each side. – 2.50 – 2.50 0.90b + 0 = 16.00 Simplify. ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Additional Examples (continued) 1 0.90b 16 = 0.90 0.90 Divide each side by 0.90. 1 1b = 17.7 Simplify. You can order 17 bulbs. 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. ALGEBRA READINESS Solving Two-Step Equations LESSON 3-4 Lesson Quiz Solve each equation. 1. 6a + 12 = 30 3 3. 4c – 40 = 28 17 2. b + 21 = 24 5 15 4. d + 15 = 22 7 49 ALGEBRA READINESS