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

Copyright Ed2Net Learning, Inc. 1

Solving Two-Step Equations

Grade 6


1.15t = 140

2.4 k =260

3. g/8= 3/26

4. 3 z =210

5.19 d = 798

Warm up


1. Isolate the variable you wish to solve for

2.Substitute your answer into the original equation and check that itworks

Steps for Solving Steps for Solving EquationsEquations

Lets review what we have learned in the last lesson


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 1Isolate the variable itself


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


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


1.Combine like terms


3.Substitute your answer into the original equation and check that it works

Steps for Solving Two step Equations

Lets get Started


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


(8y +2y) + 5 = 12

10y + 5 = 12

Example in Step 1


When the variable does not have a coefficient of one, we will need to isolate the variable itself


Step 2Step 2: Isolate the variable itself


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 The Addition Property of EqualityEquality and Its Inverse Property of Its Inverse Property of SubtractionSubtraction


(8y +2y) + 5 = 12 10y + 5 = 12 10y + 5 - 5 = 12 -5

10y = 7

Example in Step 2


=

Multiplication and Division Properties of

Equality For any real numbers a, b, and c, if a = b, then

a = b· c · c a b

Example:Example:c c

If m 4

= 6 then

4 m4

. = 4 6. If -4n = 8 then

-4n 8 -4 -4

=


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


10y + 5 = 12 10y + 5 -5 = 12 -5 10y = 7 y = 7 10

(8y +2y) + 5 = 12


Lets Solve an Example with variable term on both sides5x 2 = x + 4

5x 2 + 2 = x + 4 + 2

5x = x + 65x – x = x – x + 6 4x =

64 4x =

32

Notice that there are variables on both sidesGet rid of the -2 on the left sideSimplifyGet rid of the x on the right sideGet rid of the coefficient of x and simplifySimplify

3

2






Step 3


Example in step 3

(8y +2y) + 5 = 12Example 1 :Substituting value of y = 7 in 10the equation to check if it holds true 8 7 + 2 7 + 5 = 12

10 10 5.6 + 1.4 + 5 = 12

12 = 12


Example 2 :

Check for substitution

5x 2 = x + 4 Substituting value of x = 3 in 2the equation to check if it holds true 5 3 - 2 = 3 + 4

2 215 - 4 = 3 + 8 2 2

11 112 2

=


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


6) 12x – 3 = 8x – 19

7) -12 = 7f -5

8) 2n – 35 =106

9) n/3 -6 = 12

10) 24 = 17 – 2c

Your Turn


Break Time!!!


Title: Format: WebEx Web BrowserDouble-click to edit


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, 1945. Find this temperature in degrees Celsius by using the formula F = 1.8C + 32


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?


3) Write two different two step equations that have 1.2 as their solution


1.Combine like terms


3.Substitute your answer into the original equation and check that it works

Steps for Solving Two step Equations

Lets recap our Lesson


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


When the variable does not have a coefficient of one, we will need to isolate the variable itself


Step 2Step 2: Isolate the variable itself






Step 3


Lets solve an example2x + 3 = 4x - 12

2x + 3 - 3 = 4x - 12 – 3

2x = 4x -15 2x -4x = 4x -4x -15

-2x = -15

x = 15 2


Substituting x = 15 in the equation 2

2x + 3 = 4x - 12

2 15 + 3 = 4 15 -12 2 2

18 = 18Equation holds true for x = 15/2

Example


You had a Great Lesson Today

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