Page 52 - Math Course 1 (Book 2)

Solving Linear Equations

Mo. 8

Lesson 5
Let’s Begin

KEY CONCEPTS:
1. Solve equations with the variable on each Solve an Equation with Variables on Each Side
side.
2. Solve equations involving grouping Example
symbols.
3. Solve equations with no solution or identity.
Solve 8 + 5s = 7s – 2. Check your solution.

8 + 5s = 7s – 2 Original equation

MO. 8 - L5a 8 + 5s – 7s = 7s – 2 – 7s Subtract 7s from each
side.
Linear Equations: 8 – 2s = –2 Simplify.
Variables and Grouping Symbols 8 – 2s – 8 = –2 – 8 Subtract 8 from each side.
–2s = –10 Simplify.
Vocabulary A-Z –2s = –10 Divide each side by –2.
–2
–2
Let us learn some vocabulary

Answer s = 5 Simplify.
identity
An equation is called an identity if the equation is To check your answer, substitute 5 for s in the
true for all values of the variable. original equation.
3(r + 1) – 5 = 3r – 2
Solve an Equation with Grouping Symbols

3(r + 1) – 5 = 3r – 2 Original Equation.
Example
3r + 3 – 5 = 3r – 2 Distributive Property.

Ref exive Property of 1
3r – 2 = 3r – 2
Equality. Solve (18 + 12q) = 6 (2q – 7). Check you solution
3
Concept Summary 1
(18 + 12q) = 6 (2q – 7) Original equation
Step for Solving Equations 3
6 + 4q = 12q – 42 Distributive Property
Step 1 Simplify the expression on each side.
Use the Distributive Property as 6 + 4q – 12q = 12q – 42 – 12q Subtract 12q from
needed. each side.
6 – 8q = –42 Simplify.
Step 2 Use the Addition and/or Subtraction Subtract 6 from
Properties of Equality to get the 6 – 8q – 6 = –42 – 6 each side.
variables on one side and the
numbers without variables on the –8q = –48 Simplify.
other side. Simplify –8q = –48 Divide each side
–8 –8 by –8.
Step 3 Use the Multiplication or Division
Property of Equality to Solve. Answer q = 6 Simplify.

To check, substitute 6 for q in the original equation.

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