Solving TwoStep and 2 3 MultiStep Equations Lesson

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Solving Two-Step and 2 -3 Multi-Step Equations Lesson Objective: I will be able to

Solving Two-Step and 2 -3 Multi-Step Equations Lesson Objective: I will be able to … • Solve equations in one variable that contain more than one operation Language Objective: I will be able to … • Read, write, and listen about vocabulary, key concepts, and examples Holt Algebra 1

Solving Two-Step and 2 -3 Multi-Step Equations Notice that this equation contains multiplication and

Solving Two-Step and 2 -3 Multi-Step Equations Notice that this equation contains multiplication and addition. Equations that contain more than one operation require more than one step to solve. Identify the operations in the equation and the order in which they are applied to the variable. Then use inverse operations and work backward to undo them one at a time. Cost per CD Total cost Cost of discount card Operations in the Equation To Solve 1. First c is multiplied by 3. 95. 1. Subtract 19. 95 from both sides of the equation. 2. Then 19. 95 is added. Holt Algebra 1 2. Then divide both sides by 3. 95.

Solving Two-Step and 2 -3 Multi-Step Equations Page 18 Backward Order of Operations to

Solving Two-Step and 2 -3 Multi-Step Equations Page 18 Backward Order of Operations to Solve Equation Order of Operations in Equation First: Addition and Subtraction Parentheses Second: Multiplication and Division Exponents Third: Exponents Multiplication and Division Fourth: Parentheses Addition and Subtraction Holt Algebra 1

Solving Two-Step and 2 -3 Multi-Step Equations Page 19 Example 1: Solving Two-Step Equations

Solving Two-Step and 2 -3 Multi-Step Equations Page 19 Example 1: Solving Two-Step Equations Solve each equation. A. 18 = 4 a + 10. – 10 8 = 4 a 4 4 First a is multiplied by 4. Then 10 is added. Work backward: Subtract 10 from both sides. Since a is multiplied by 4, divide both sides by 4 to undo the multiplication. 2=a B. 5 t – 2 = – 32. +2 +2 5 t = – 30 5 5 t = – 6 Holt Algebra 1 First t is multiplied by 5. Then 2 is subtracted. Work backward: Add 2 to both sides. Since t is multiplied by 5, divide both sides by 5 to undo the multiplication.

Solving Two-Step and 2 -3 Multi-Step Equations Page 19 Your Turn 1 Solve –

Solving Two-Step and 2 -3 Multi-Step Equations Page 19 Your Turn 1 Solve – 4 + 7 x = 3 +4 +4 7 x = 7 7 7 x=1 Holt Algebra 1 First x is multiplied by 7. Then – 4 is added. Work backward: Add 4 to both sides. Since x is multiplied by 7, divide both sides by 7 to undo the multiplication.

Solving Two-Step and 2 -3 Multi-Step Equations Example 2 A: Solving Two-Step Equations That

Solving Two-Step and 2 -3 Multi-Step Equations Example 2 A: Solving Two-Step Equations That Contain Fractions Page 20 Solve . Method 1 Use fraction operations. 3 Since 4 is subtracted from y , add 3 to 8 4 both sides to undo the subtraction. Since y is divided by 8, multiply both sides by 8 to undo the division. Holt Algebra 1 Simplify.

Solving Two-Step and 2 -3 Multi-Step Equations Page 20 Solve Example 2 B: Solving

Solving Two-Step and 2 -3 Multi-Step Equations Page 20 Solve Example 2 B: Solving Two-Step Equations That Contain Fractions. Method 2 Multiply by the LCD to clear the fractions. Multiply both Since r is multiplied sides by 12, by 8, divide both the LCD of the sides by 8 to undo fractions. the multiplication. Distribute 12 on 8 r = – 2 the left side. 8 8 Simplify. Since 9 8 r + 9 = 7 is added to 8 r, – 9 subtract 9 from 8 r = – 2 both sides to undo the addition. Holt Algebra 1

Solving Two-Step and 2 -3 Multi-Step Equations Your Turn 2 Page 21 Solve .

Solving Two-Step and 2 -3 Multi-Step Equations Your Turn 2 Page 21 Solve . Method 2 Multiply by the LCD to clear the fractions. Multiply both sides by 10, the LCD of the fractions. Distribute 10 on the left side. 4 x – 5 = 50 +5 +5 4 x = 55 Holt Algebra 1 Simplify. Since 5 is subtracted from 4 x, add 5 to both sides to undo the subtraction. Simplify. Since 4 is multiplied by x, divide both sides by 4 to undo the multiplication. 4 x = 55 4 4

Solving Two-Step and 2 -3 Multi-Step Equations that are more complicated may have to

Solving Two-Step and 2 -3 Multi-Step Equations that are more complicated may have to be simplified before they can be solved. You may have to use the Distributive Property or combine like terms before you begin using inverse operations. Holt Algebra 1

Solving Two-Step and 2 -3 Multi-Step Equations Example 3: Simplifying Before Solving Equations Solve

Solving Two-Step and 2 -3 Multi-Step Equations Example 3: Simplifying Before Solving Equations Solve 10 y – (4 y + 8) = – 20 Page 21 10 y + (– 1)(4 y + 8) = – 20 Write subtraction as addition of the opposite. 10 y + (– 1)(4 y) + (– 1)( 8) = – 20 Distribute – 1 on the left side. 10 y – 4 y – 8 = – 20 Simplify. 6 y – 8 = – 20 Combine like terms. +8 + 8 Since 8 is subtracted from 6 y, add 8 to both sides to undo 6 y = – 12 6 6 y = – 2 Holt Algebra 1 the subtraction. Since y is multiplied by 6, divide both sides by 6 to undo the multiplication.

Solving Two-Step and 2 -3 Multi-Step Equations Your Turn 3 Page 22 Solve 4(x

Solving Two-Step and 2 -3 Multi-Step Equations Your Turn 3 Page 22 Solve 4(x – 2) + 2 x = 40 (4)(x) + (4)(– 2) + 2 x = 40 4 x – 8 + 2 x = 40 4 x + 2 x – 8 6 x – 8 +8 6 x = 40 +8 = 48 6 x = 48 6 6 x=8 Holt Algebra 1 Distribute 4 on the left side. Simplify. Commutative Property of Addition. Combine like terms. Since 8 is subtracted from 6 x, add 8 to both sides to undo the subtraction. Since x is multiplied by 6, divide both sides by 6 to undo the multiplication.

Solving Two-Step and 2 -3 Multi-Step Equations Example 4: Solving Equations to Find an

Solving Two-Step and 2 -3 Multi-Step Equations Example 4: Solving Equations to Find an Indicated Value If 4 a + 0. 2 = 5, find the value of a – 1. Page 22 Step 1 Find the value of a. 4 a + 0. 2 = 5 Since 0. 2 is added to 4 a, subtract 0. 2 – 0. 2 from both sides to undo the addition. 4 a = 4. 8 Since a is multiplied by 4, divide both sides by 4 to undo the multiplication. a = 1. 2 Step 2 Find the value of a – 1. 1. 2 – 1 To find the value of a – 1, substitute 1. 2 for a. Simplify. 0. 2 Holt Algebra 1

Solving Two-Step and 2 -3 Multi-Step Equations Classwork Assignment #5 • Holt 2 -3

Solving Two-Step and 2 -3 Multi-Step Equations Classwork Assignment #5 • Holt 2 -3 #4, 10, 16, 19, 22 Holt Algebra 1