Page 157 - Math Course 1 (Book 1)

Equations with Grouping Symbols

Mo. 5

Lesson 2

Let’s Begin
KEY CONCEPTS:
1. Solve equations that involve grouping
symbols.
2. Use equations that involve grouping Solve Equations with Parentheses
symbols to solve a problem.
3. Identify equations that have no solution or Examples
an inf nite number of solutions.
Solve 3h = 5(h – 2). Check your solution.
MO. 5 - L2a 3h = 5(h – 2) Write the equation.

Solving Equations with 3h = 5(h) – 5(2) Use the Distributive

Variables property.

3h = 5h – 10 Simplify.
Vocabulary A-Z 3h – 5h = 5h – 5h – 10 Subtract 5h from each side.
Let us learn some vocabulary

–2h = –10 Simplify.
-2h = -10 Divide each side by –2.
Identity -2 -2
h = 5 Simplify.
An equation that is true for every value of the
variable is called an identity. Check

Solve 2(2x - 1) + 6 = 4x + 4 3h = 5(h – 2) Write the equation.
2(2x - 1) + 6 = 4x + 4 Write the equation.
3(5) = 5(5 – 2) Replace h with 5.

4x - 2 + 6 = 4x + 4 Use the Distributive Simplify.
Property. 15 = 5(3)

4x + 4 = 4x + 4 Simplify. 15 = 15 This statement is true.

4x + 4 - 4 = 4x + 4 - 4 Subtract 4 from each
side.

4x = 4x Simplify. Answer The solution is 5.
x = x Mentally divide each
side by 4. Solve 6(b – 2) = 3(b + 8.5). Check your solution.
The sentence x = x is always true.
The solution set is all numbers. 6(b – 2) = 3(b + 8.5) Write the equation.

Grouping Symbols 6b – 12 = 3b + 25.5 Use the Distributive
Property.
All the same and are called grouping symbols:
Brackets : [ ] These all mean multiply: 6b – 12 – 3b = 3b – 3b + 25.5 Subtract 3b from
Parenthesis : ( ) 3 x 3 3 • 3 3(3) each side.
Braces: { }
3b – 12 = 25.5 Simplify.
Remember:
3b – 12 + 12 = 25.5 + 12 Add 12 to each side.
Work grouping symbols from the inside out
9 - [ 4(3 + 2) ] = 9 - [ 4(5) ] = 9 - 20 3b = 37.5 Simplify.
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