Study Guide Day 5: Open Sentences

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Mathematical statements with one or more variables, or unknown numbers, are called open sentences. An open sentence is neither true nor false until the variable has been replaced by a value. Finding a replacement for the variable that results in a true sentence is called solving the open sentence This replacement is called the solution of the open sentence.

Replace b in 6b + 7 = 37 with the valves 3, 4, 5, and 6. Then see whether each replace replacement results in a true or false sentence.
Replace b with:	6b + 7 = 37	True? or False?
3	6(3) + 7 = ?37 = 25 ≠ 37	False
4	6(4) + 7 = ?37 = 31 ≠ 37	False
5	*6(5) + 7 =?37* = 37**	True
6	6(6) + 7 =?37 = 43 ≠ 37	False
Since b = 5 makes the sentence 6b + 7 = 37 true, the solution set for 6b + 7 =37 is {b\| 5 }.

A set of numbers from which replacements for a variable may be chosen is called a replacement set. The set of all replacements for the variable in an open sentence that results in a true sentence is called the solution set for the sentence.

A sentence that contains an equals sign, "=", is called an equation and sometimes may be solved by simply applying the order of operations. A sentence having the symbols < or > is called an inequality.