13 Open Sentences

1
1-3 Open Sentences
Be smart -correct your odd homework problems
after you complete them!
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
A mathematical statement with one or more
variables is called and open sentence.
An open sentence with an equal sign, , is an
equation.
An open sentence with the symbol lt, lt, gt, or gt is
an inequality.
3
An open sentence is neither true nor false until
the variable/s have been replaced by specific
values. The process of finding a value for the
variable that results in a true sentence is
called solving the open sentence. This
replacement value is called a solution.
The value or values of the variable that make the
statement true is the solution.
4
A set of numbers from which replacements for a
variable may be chosen is called a replacement
set. A set is a collection of numbers. It is
often shown using braces, . Each number in
the set is called an element, or member. The
solution set of an open sentence is the set of
elements from the replacement set that makes the
open sentence true.
Replacement set 3, 4, 5, 6, 7
Solution set is 5, 6, 7.
Solution set is 5.
The value or values of the variable that make the
statement true is the solution.
5
To solve an equation given a replacement set,
substitute each value into the equation and
simplify to determine if it makes the equation a
true statement.
Find the solution set for 6n 7 gt 37 if the
replacement set is 4, 5, 6, 7
5
The value or values of the variable that make the
statement true is the solution.
6
Example 1 Find the solution set for 5(x 2) 40
if the replacement set is 4, 5, 6, 7
6
The value or values of the variable that make the
statement true is the solution.
7
An inequality is a statement formed by placing an
inequality symbol between two expressions.
inequality symbol meaning example
lt is less than 4 lt 8
lt is less than or equal to 4 lt 8
gt is greater than 20 gt 5
gt is greater than or equal to 20 gt 5
Whats the importance of is in each of the above?
It represents the verb in the statement. Without
it you will have an expression not a statement.
8
Beware of inequality versus subtraction.
n less than 4
expression
4
-
n
(translation)
n is less than 4
sentence
lt
4
n
(translation)
Copy in your spiral notebook!
Is this an expression or a sentence?
Is this an expression or a sentence?
9
To solve an inequality given a replacement set,
substitute each value into the inequality and
simplify to determine if it makes the inequality
a true statement.
Find the solution set for 30 n gt 37 if the
replacement set is 5, 6, 7, 8
7, 8
The value or values of the variable that make the
statement true is the solution.
10
Example 2 Find the solution set for 9 gt 2y - 5 if
the replacement set is 5, 6, 7, 8
5, 6
The value or values of the variable that make the
statement true is the solution.
11
Solve the equation by applying the order of
operations.
Write the problem.
Follow rules for order of operations.
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Solve.
Example 3
Example 4
Example 5
13
Solve.
Example 7
Example 6
14
Homework

• 1-A5 Pages 18-19 22-37,53-59.