Copyright Ed2Net Learning, Inc. 1 Solving Two-Step Equations Grade 6

Copyright Ed2Net Learning, Inc t = k = g/8= 3/ z = d = 798 Warm up

Copyright Ed2Net Learning, Inc.3 1. Isolate the variable you wish to solve for 2.Substitute your answer into the original equation and check that it works Steps for Solving Equations Lets review what we have learned in the last lesson

Copyright Ed2Net Learning, Inc.4 If the variable does not have a coefficient of one, we will need to isolate the variable itself When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable Step 1 Isolate the variable itself

Copyright Ed2Net Learning, Inc.5 If a = b, then ac = bc where c = 0 If c = d, then c/e = d/e where e = 0 Multiplying both sides of an equation by the same nonzero number produces an equivalent equation The Multiplication Property of Equality and The Inverse Operation of Division

Copyright Ed2Net Learning, Inc.6 Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions By substituting, we switch or exchange values, often replacing a variable with a numerical value We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation Step 2

Copyright Ed2Net Learning, Inc.7 1.Combine like terms 2. Isolate the variable you wish to solve for 3.Substitute your answer into the original equation and check that it works Steps for Solving Two step Equations Lets get Started

Copyright Ed2Net Learning, Inc.8 Step 1: Combine Like Terms Combine together the terms containing the variable Like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient. Step 1

Copyright Ed2Net Learning, Inc.9 (8y +2y) + 5 = 12 10y + 5 = 12 Example in Step 1

Copyright Ed2Net Learning, Inc.10 When the variable does not have a coefficient of one, we will need to isolate the variable itself When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable Step 2 Step 2: Isolate the variable itself

Copyright Ed2Net Learning, Inc.11 If a = b, then a + c = b + c If a = b, then a – d = b – d Adding the same quantity to both sides of an equation produces an equivalent equation Subtraction is simply adding a negative number, this rule applies when subtracting the same quantity from both sides The Addition Property of Equality and Its Inverse Property of Subtraction

Copyright Ed2Net Learning, Inc.12 (8y +2y) + 5 = 12 10y + 5 = 12 10y = y = 7 Example in Step 2

Copyright Ed2Net Learning, Inc.13 = Multiplication and Division Properties of Equality For any real numbers a, b, and c, if a = b, then a = b· c a b Example: cc If m 4 = 6then 4 m4m4. =4 6. If -4n = 8 then -4n =

Copyright Ed2Net Learning, Inc.14 If a = b, then ac = bc where c = 0 If c = d, then c = d where e = 0 e e Multiplying both sides of an equation by the same nonzero number produces an equivalent equation The Multiplication Property of Equality and The Inverse Operation of Division

Copyright Ed2Net Learning, Inc.15 10y + 5 = 12 10y = y = 7 y = 7 10 (8y +2y) + 5 = 12

Copyright Ed2Net Learning, Inc.16 Lets Solve an Example with variable term on both sides 5x  2 = x + 4 5x  = x x = x + 6 5x – x = x – x + 6 4x = 6 4 x = 3232 Notice that there are variables on both sides Get rid of the -2 on the left side Simplify Get rid of the x on the right side Get rid of the coefficient of x and simplify Simplify 3 2

Copyright Ed2Net Learning, Inc.17 Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions By substituting, we switch or exchange values, often replacing a variable with a numerical value We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation Step 3

Copyright Ed2Net Learning, Inc.18 Example in step 3 (8y +2y) + 5 = 12 Example 1 : Substituting value of y = 7 in 10 the equation to check if it holds true = = = 12

Copyright Ed2Net Learning, Inc.19 Example 2 : Check for substitution 5x  2 = x + 4 Substituting value of x = 3 in 2 the equation to check if it holds true = = =

Copyright Ed2Net Learning, Inc.20 Your Turn 1)2c – 3 = 5 2)9y + 4 = 4 3)8w – 2 = -2 4)0.5 (y-3) = 12 5)2w + 4 = 3w – 8

Copyright Ed2Net Learning, Inc.21 6) 12x – 3 = 8x – 19 7) -12 = 7f -5 8) 2n – 35 =106 9) n/3 -6 = 12 10) 24 = 17 – 2c Your Turn

Copyright Ed2Net Learning, Inc.22 Break Time!!!

Copyright Ed2Net Learning, Inc.23

Copyright Ed2Net Learning, Inc.24 1)Temperature is usually measured on the Fahrenheit (°F) or the Celsius scale (°C). The highest temperature ever recorded in Orlando, Florida, was 102°F in May, Find this temperature in degrees Celsius by using the formula F = 1.8C + 32

Copyright Ed2Net Learning, Inc.25 2) Benny’s balloons charges $2 for each balloon in an arrangement. There is also a $5 fee for making the arrangement. If you have $15 to spend, how many balloons would you get?

Copyright Ed2Net Learning, Inc.26 3) Write two different two step equations that have 1.2 as their solution

Copyright Ed2Net Learning, Inc.27 1.Combine like terms 2. Isolate the variable you wish to solve for 3.Substitute your answer into the original equation and check that it works Steps for Solving Two step Equations Lets recap our Lesson

Copyright Ed2Net Learning, Inc.28 Step 1: Combine Like Terms Combine together the terms containing the variable Like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient. Step 1

Copyright Ed2Net Learning, Inc.29 When the variable does not have a coefficient of one, we will need to isolate the variable itself When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable Step 2 Step 2: Isolate the variable itself

Copyright Ed2Net Learning, Inc.30 Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions By substituting, we switch or exchange values, often replacing a variable with a numerical value We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation Step 3

Copyright Ed2Net Learning, Inc.31 Lets solve an example 2x + 3 = 4x x = 4x - 12 – 3 2x = 4x -15 2x -4x = 4x -4x x = -15 x = 15 2

Copyright Ed2Net Learning, Inc.32 Substituting x = 15 in the equation 2 2x + 3 = 4x = = 18 Equation holds true for x = 15/2 Example

Copyright Ed2Net Learning, Inc.33 You had a Great Lesson Today