LOG 1 Lesson A: Solving Multi-Step Equations

LOG 1 Lesson A: Solving Multi-Step Equations

by

​Kimberly English

​State Standards

AREI.3* Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

​

AREI.1* Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

​

​Objectives

​Students will be able to

(1) solve multi-step equations in one variable.

(2) justify the steps taken when solving multi-step equations.

​Prerequisite Skills Needed

​Students must be able to:

​

​1) Add, subtract, multiply and divide integers. IXL Grade 8 C.3 and C.7

​2) Identify constants and coefficients. https://bit.ly/3BsbJNL

​3) Combine like terms. https://bit.ly/3vPEvq7

​4) Apply the distributive property. IXL Grade 8 X.13

​4) Solve two step equations. IXL Grade 7 S.6

​5) Solve one step equations. IXL Grade 7 S.7

Solving Multi-Step Equations

​Take out your notes labeled Solving Linear Equations Flowchart

​How to Solve a Multi-Step Equation

​Step 1

​Simplify each side of the equation, if necessary.

​

​Step 2

​Use the inverse operation to isolate the variable.

​FLOWCHART

​Step 1

​See if you have the following: Rational expression with a constant in the denominator, parentheses, like terms.

​

​Step 2

​Isolate the variable by adding or subtracting the constant on the same side as the variable then dividing or multiplying the coefficient.

Example #1

​Solve the equation and justify each step.

​

​21 = 1 - 6x + 8

​​Step 1

​Simplify each side of the equation.

​Combine Like Terms:

​21 = 1 - 6x + 8

​21 = 9 - 6x Justify: Equivalent Equation

​

​Step 2

​Use the inverse operation to isolate the variable.

​Constant on the Same Side as Variable:

​​21 = 9 - 6x

​- 9 -9

12 = -6x Justify: Subtraction Property of Equality

​​Coefficient:

​ 12 = -6x

​-6 -6 Justify: Division Property of Equality

​-2 = x

Example #2

​Solve the equation and justify each step.

​

​5n + 4 - 2n = -11

​​Step 1

​Simplify each side of the equation.

​Combine Like Terms:

​5n + 4 - 2n = -11

​3n + 4 = -11 Justify: Equivalent Equation

​

​Step 2

​Use the inverse operation to isolate the variable.

​Constant on the Same Side as Variable:

​​3n + 4 = -11

​ - 4 - 4

3n = -15 Justify: Subtraction Property of Equality

​​Coefficient:

​ 3n = -15

​ 3 3 Justify: Division Property of Equality

​n = -5

Example #3

​Solve the equation and justify each step.

​

​140 = 8(1 - 4n) + 4

​​Step 1

​Simplify each side of the equation.

Parentheses - Distributive Property

​140 = 8 - 32n + 4

Combine Like Terms:

​140 = 8 - 32n + 4

​140 = 12 - 32n Justify: Equivalent Equation

​

​Step 2

​Use the inverse operation to isolate the variable.

​Constant on the Same Side as Variable:

​​ 140 = 12 - 32n

​ - 12 - 12

128 = -32n Justify: Subtraction Property of Equality

​​Coefficient:

​128 = -32n

-32 -32 Justify: Division Property of Equality

​n = -5

Example #4

​Solve the equation and justify each step.

​

​-5(4x - 2) - 5x = -165

​​Step 1

​Simplify each side of the equation.

Parentheses - Distributive Property

​-20x + 10 - 5x = -165

Combine Like Terms:

-20x + 10 - 5x = -165

​-25x + 10 = -165 Justify: Equivalent Equation

​

​Step 2

​Use the inverse operation to isolate the variable.

​Constant on the Same Side as Variable:

​​ -25x + 10 = -165

​ - 10 - 10

-25x = -175 Justify: Subtraction Property of Equality

​​Coefficient:

​-25x = -175

-25 -25 Justify: Division Property of Equality

​x = 7

Example #5

​Solve the equation and justify each step.

​

​-(k + 3) + 4 = 92

​​Step 1

​Simplify each side of the equation.

Parentheses - Distributive Property

​-1(k + 3) + 4 = 92

-1k - 3 + 4 = 92

Combine Like Terms:

-1k - 3 + 4 = 92

​-1k + 1 = 92 Justify: Equivalent Equation

​

​Step 2

​Use the inverse operation to isolate the variable.

​Constant on the Same Side as Variable:

​​ -1k + 1 = 92

​ -1 -1

-1k = 91 Justify: Subtraction Property of Equality

​​Coefficient:

​-1k = 91

-1 -1 Justify: Division Property of Equality

​k = -91

Multiple Choice

What would be the correct first step to solving this equation:  2x - 4 + x = 5

• Distributive Property - Distribute the 2x

• Subtract 4 from both sides of the equation.

• Add x to both sides of the equation.

• Combine Like Terms: 2x and x.

Multiple Select

Which of the following steps will be used to solve the equation: 1 + 2(x - 4) = 7

• Distributive Property - Distribute the 2

• Division Property of Equality - Divide both sides of the equation by 2.

• Addition Property of Equality: Add 7 to both sides of the equation.

• Combine Like Terms: 1 and -8.

Example #6

​The sum means to add. Therefore we will add all the angles.

​6x + 6 + 12x - 8 + 100 + 100 = 360

​

​Combine like terms: 18x + 198 = 360

​Eliminate the constant on the same side as the variable: 198

​18x + 198 = 360

​ - 198 -198

​18x = 162

​Eliminate the Coefficient: 18

​​18x = 162

​ 18 18

​x = 9

​The sum of the angle measures of a quadrilateral is 360. Solve for x.

Example #6

​The sum means to add. Therefore we will add all the angles.

50 + 80 + 9x + 5 = 180

​

​Combine like terms: 9x + 135 = 180

​Eliminate the constant on the same side as the variable: 135

​9x + 135 = 180

​ - 135 -135

​9x = 45

​Eliminate the Coefficient: 9

​​9x = 45

​ 9 9

​x = 5

​The sum of the angle measures of a triangle is 180. Solve for x.

Multiple Choice

True or False: To find the sum of the angles of the triangle, the equation will be written as 4x + 2x - 60 = 180.

• True

• False

If you need more assistance, please come to tutoring on Tuesday or Thursday afternoons in Room 514​ or attend the LIVE Google Meet.