Unit 05: Equations and Inequalities

Unit 06: Equations and Inequalities

Key Vocabulary

This includes vocabulary that is new to this unit as well as vocabulary that was introduced in prior units.

6.13, 7.12

• coefficient - the number that is being multiplied by the variable

• equation - numerical sentence that contains an equal sign

• expression - numbers, symbols, and operators that are grouped together

• inverse - the opposite

• numerical expression - an expression that contains no variables

• term - terms are separated by +, -, or = signs

• variable - a symbol we don't know yet. Variables are represented by alphabetic letters.

• variable expression - an expression that contains one or more variables

• numerical expression - an expression that contains numbers and no variables

• inverse operations - operations that undo each other

6.14, 7.13

• inequality - the relationship between two expression that are not equal

• solution set - a set of answers

Properties of Real Numbers

• 6.13, 7.12

• associative property of addition and multiplication - you can add or multiply regardless of how the numbers are grouped.

• commutative property of addition – it doesn’t matter in what order you add numbers.

• commutative property of multiplication - it doesn't matter in what order you multiply numbers.

• distributive property of multiplication - when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately.

• additive identity property (identity property of addition) - adding zero does not change the original number.

• multiplicative identity property (identity property of multiplication) - multiplying by one does not change the original number.

• multiplicative inverse property (inverse property of multiplication) - multiplying by the inverse equals one.

• multiplicative property of zero – multiplying by zero equals zero.

Properties of Equality

6.13, 7.12

• addition property of equality - if the same amount is added to both sides of the equation, the equality is still true

• subtraction property of equality - if the same amount is subtracted both sides of the equation, the equality is still true

• multiplication property of equality - if the same amount is multiplied to both sides of the equation, the equality is still true

• division property of equality - if the same amount is divide by both sides of the equation, the equality is still true

Properties of Inequality

6.14

• addition property of inequality - if the same amount is added to both sides of the inequality, the inequality is still true

• subtraction property of inequality - if the same amount is subtracted from both sides of the inequality, the inequality is still true

7.13

• multiplication property of inequality - you can multiply both sides of an inequality by the same number, but if you multiply the coefficient by a negative number, you must flip the inequality sign

• division property of inequality - you can divide both sides of an inequality by a the same number, but if you divide the coefficient by a negative number, you must flip the inequality sign