Page 28 - Math Course 1 (Book 2)

Solving Open Sentence Equations

Mo. 7

Lesson 5 set

is a collection of objects or numbers. It is often
shown using braces, { }.
{3, 4, 5}
KEY CONCEPTS:
1. Solve open sentence equations. In this statement the collection of numbers are in
braces.
2. Solve open sentence inequalities.

element
each number in the set is called an element, or
member.
MO. 7 - L5a
{3, 4, 5}
Solve Open Sentence Equations In this statement 3, 4, 5 are the elements

solution set
Vocabulary A-Z of an open sentence is the set of elements from

Let us learn some vocabulary the replacement set that make the open sentence
true.

n 6n + 7 = 37 True or False

open sentence
3 6(3) + 7 ≟ 37 → 25 ≠ 37 false
a mathematical statement with one or more
variables is called an open sentence.
4 6(4) + 7 ≟ 37 → 31 ≠ 37 false
6n + 7 = 37

5 6(5) + 7 ≟ 37 → 37 = 37 true !
In the above statement the letter n is a variable.
In this example { 5 } is the solution set.
solving an open sentence
the process of f nding a value for a variable that
results in a true sentence is called solving the open
sentence.

n 6n + 7 = 37 True or False
Let’s Begin

3 6(3) + 7 ≟ 37 → 25 ≠ 37 false
! Use a Replacement Set to Solve an Equation
5 6(5) + 7 ≟ 37 → 37 = 37 true

solution Examples
the replacement value is called a solution.
Find the solution set for 4a + 7 = 23 if the
n 6n + 7 = 37 True or False replacement set is {2, 3, 4, 5, 6}.

Replace a in 4a + 7 = 23 with each value in the
3 6(3) + 7 ≟ 37 → 25 ≠ 37 false replacement set.
!
5 6(5) + 7 ≟ 37 → 37 = 37 true

In the above statement the letter n is a replacement
value.
20