Post on 31-Mar-2015
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1-3 Open Sentences
Be smart -correct your
odd homework problems after you complete
them!
Algebra 1 Glencoe McGraw-Hill Linda Stamper
A mathematical statement with one or more variables is called an open sentence.
1510xExample An open sentence with an equal sign, =, is an equation.
1510xExample
An open sentence with the symbol <, <, >, or > is an inequality.
An open sentence is neither true nor false until the variable/s have been replaced by specific values.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 solutionsolution.
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.
1510x
The value or values of the variable that make the statement true is the solutionsolution.
1510x Replacement set {3, 4, 5, 6, 7}
Solution set is {5}.
Solution set is {5, 6, 7}.
To solve an equation given a replacement set, substitute eacheach value into the equation and simplify to determine if it makes the equation a true statement.
The value or values of the variable that make the statement true is the solutionsolution.
Find the solution set for 6n + 7 = 37 if the replacement set is {4, 5, 6, 7}
{5}
3731
37724
37746
377n6
3737
37730
37756
377n6
3743
37736
37766
377n6
3749
37742
37776
377n6
The value or values of the variable that make the statement true is the solutionsolution.
Example 1 Find the solution set for 5(x + 2) = 40 if the replacement set is {4, 5, 6, 7}
{6}
4030
4065
40245
402x5
4035
4075
40255
402x5
4040
4085
40265
402x5
4045
4095
40275
402x5
An inequality is a statement formed by placing an inequality symbol between two expressions.
< is less than 4 < 8
< is less than or equal to 4 < 8 > is greater than 20 > 5
> is greater than or equal to 20 > 5
inequality symbol meaning example
What’s 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.
n is less than 4
Beware of inequality versus subtraction.
n less than 4
expression
Is this an expression or a
sentence?
4−n(translation)
Is this an expression or a
sentence?
sentence(translation)
n < 4
Copy in your spiral notebook!
To solve an inequality given a replacement set, substitute eacheach value into the inequality and simplify to determine if it makes the inequality a true statement.
The value or values of the variable that make the statement true is the solutionsolution.
Find the solution set for 30 + n > 37 if the replacement set is {5, 6, 7, 8}
{7, 8}
3735
37530
37n30
3736
37630
37n30
3737
37730
37n30
3738
37830
37n30
The value or values of the variable that make the statement true is the solutionsolution.
Example 2 Find the solution set for 9 > 2y − 5 if the replacement set is {5, 6, 7, 8}
{5, 6}
59
5109
5529
5y29
79
5129
5629
5y29
99
5149
5729
5y29
119
5169
5829
5y29
Write the problem.Follow rules for order of operations.
Solve the equation by applying the order of operations.
4534213
m
13813
321
7
Solve.
Example 3
Example 4
Example 5
129
y2
1243573
x2
k3518
2853
381
27
1243
579
343
29
31229
157
3218
105
818105
1050
5
Solve.
Example 6
424
3425x 3
2
484
3445
44
3420
161220
1632
2
32931831
34y
Solve.
3295431
34
326331
34
86331
34
86331
12
82112
89 1
Example 7
Solve.
128.088.07m 128.88.07
128.86.5
124.14
4.2
Example 8
Solve.
2314584486364212438
y
61458448
624212438
7458448
62442438
2858448
6842438
338448
634438
26444840438
18416024
184184
1
Example 9
1-A5 Pages 18-20 #22-37,53-59.