Chapter 1 : Linear Equations

For any real numbers a, b, and c if a>b the a + c > b + c

for any real number a, a = a

Contains variables, numbers, and operations

Contains words to express mathematical information

when infinity symbols are used to indicate that a set is unbounded in the positive or negative direction

replacement for variable in an open sentence that makes the sentence true

two or more inequalities connected by the words and or or

a mathematical sentence containing one or more variables

If a a = b, then a may be required by b and b may be replaced by a

For any real numbers a, b, and c, c does not equal 0; if a = b then a x c = b x c and a/c = b/c

For all real numbers a and b if a = b then b = a

For any real numbers a, b, and c if a>b the a - c > b - c

For all real numbers a, b, and c if a = b and b = c then a = c

a mathematical sentence stating that two mathematical expressions are equal

For any real numbers a, b, c, if a = b then a + c = b + c and a - c = b - c