A statement is any sentence that is either true or false, but not both. Look at the sentences below. Are they true or false?
You can choose symbols to express mathematical statements.
Words Symbols
A number m minus 5 is equal to 12. m – 5 = 12
20 equals a number y plus 4. 20 = y
+ 4
Eight increased by a number d is 6. 8
+ d = 6
Seven minus a number equals 5. 7 – x = 5
The sum of a number and 11 equals 20.
z
+ 11 = 20
Mathematical sentences like these are called open sentences. An open
sentence is neither true nor false until the variable is replaced by a value. A
set of numbers from which replacements for a variable may be chosen is called a
replacement set.
Finding the replacements for the variable that results in a true sentence is
called solving the open sentence. The replacement values are called a solution of the open
sentence.
Example
1.
Find
the solution of m – 5 = 12 if the
replacement set is {15, 16, 17, 18}.
Alternative Solutions :
Since 17
makes the sentence m – 5 = 12 true, the solution is 17.
2.
Find
the solution of 2n + 3 = 9 if the
replacement set is {2, 3, 4, 5}.
Alternative Solutions :
Therefore,
the solution of 2n + 3 = 9 is 3.
Open sentences and replacement sets are used frequently in
real-life situations.
Example
Health Link
3. The
normal systolic blood pressure p of a
woman who is A years old is given by
the formula 
. Ms. Adams recently had her annual physical. Her blood
pressure was normal. If Ms. Adams’ blood pressure was 121, how old is she: 34,
35, 36, or 37?
Alternative Solutions :
You
need to find the replacement for the variable that results in a true sentence.
First, replace p with 121.
Then
replace A with each of the replacements.
The
solution is 35. So, Ms. Adams is 35 years old.
Recall that an open sentence containing an equals sign, =, is
an equation. Sometimes, you can solve an equation by simply applying the
order of operations.
Example
4.
4(8)
+ 6 = a
Alternative Solutions :
4(8) + 6 = a Original
equation
32
+
6 = a Multiply 4 and 8.
38 = a Add
32 and 6.
The
solution is 38.
Sumber
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