Chapter 01 Section 05

1
Chapter 01 Section 05

• Open Sentences

2
1-5 OPEN SENTENCES
OBJECTIVES
To solve open sentences by performing
arithmetic operations.

• open sentence - a mathematical statement with
  one or more variables
• the variable has to be replaced by a value
• solving the open sentence - the process of
  finding out what number the variable is holding
  place for
• solution - the replacement value for the
  variable in an open sentence

CLARIFICATION An open sentence in mathematics
is like an English sentence with a blank in it.
The sentence __________________ is a color. is
true if Blue is placed in the blank, false if
Hard is placed in the blank, and neither true nor
false if the blank is left empty.
3
1-5 OPEN SENTENCES
More terms you will be using in this section

• replacement set - a set of numbers (one or more)
  which make an open sentence true
• set - a collection of objects or numbers
• element - each individual object in a set
• solution set - all the replacement values that
  make an open sentence become true

4
1-5 OPEN SENTENCES
A replacement set is the group of numbers you
will be plugging in to look for the solutions.
The solution set is the group of numbers that
worked when they were plugged in. Solution
sets are the values that make the sentence a true
statement. The numbers 4, 5, 6, 7, and 8 are all
elements of this set 4, 5, 6, 7, 8 Notice
that we use brackets to surround sets when we
list them.
5
1-5 OPEN SENTENCES
EX1ß
EXAMPLE 1a Find the solution set for y 5 lt 7
if the replacement set is 0, 1, 2, 3, 4.
For these problems, it will help to make a chart.
0 5 5
TRUE
1 5 6
TRUE
2 5 7
TRUE
3 5 8
FALSE
4 5 9
FALSE
The solution set for y 5 ? 7 is 0, 1, 2.
Word of Caution The book uses 0 to answer
solutions sets of . To say 0 is the solution
set is not the same as saying 0 is the solution
set. Plain 0 means there were no true
replacements. 0 means the only true
replacement was 0 from the replacement set.
6
1-5 OPEN SENTENCES
EXAMPLE 1ß Find the solution set for
if the replacement set is 0, 2, 4, 6,
8.
7
1-5 OPEN SENTENCES
EX2ß
We can use order of operations to find values for
variables when we set a single variable equal to
algebraic expressions.
KEY NOTE You can only solve for one variable
with one equation.
Focus on the numerator.
Focus on the denominator.
Numerator divided by denominator.
5(3 5)
3 2 2
Parenthesis first.
Multiply first.
d 5 or The solution is 5.
5(8)
6 2
Multiply.
Add.
40
8
8
1-5 OPEN SENTENCES
EXAMPLE 2ß Solve each equation. a. b.
9
1-5 OPEN SENTENCES
HOMEWORK
PAGE 35 13 31 odd