Expressions and Equations

Graph of an Inequality

A graph that shows all of the solutions of an inequality on a number line.

Expression

A mathematical phrase containing numbers, operations, and/or variables. Examples: 12+6,18+3×4, 8+x, 6×a-b

Algebraic (Expression)

A mathematical phrase that includes one or more variables.

Inequality

A mathematical sentence that compares expressions. It contains the symbols <,>,≤,or ≥. Examples: x-4<-14, x+5≥-67

Equation

A mathematical sentence that uses an equal sign, =, to show that two expressions are equal. 4x=16, a+7=21

Coefficient

A number which multiplies a variable. 3 is the coefficient in 3x.

Variable

A symbol, usually a letter, that represents a quantity or number. x is a variable in 2x+1.

Constant

A term that has a number but no variable. In the expression 2x+8, the term 8 is a constant term.

Variable Term

A term that has a variable. In the expression 2x+8, the term 2x is a variable term.

Solution (of an equation)

A value that makes an equation true. 6 is the solution of the equation x-4=2.

Simplest Form (of an algebraic expression)

An algebraic expression is in simplest form if it has no like terms and no parentheses. 6-9a,3t+5

Numerical Expression

An expression that contains only numbers and operations (no variables). Examples: 12+6,18+3×4

Equivalent Equations

Equations that have the same solution(s). 2x-8=0 and 2x=8

Equivalent Expressions

Expressions with the same value.

Division Property of Inequality

If you divide each side of an inequality by the same positive number, the inequality remains true. If you divide each side of an inequality by the same negative number, the inequality symbol must be reversed for the inequality to remain true.

Multiplication Property of Inequality

If you multiply each side of an inequality by the same positive number, the inequality remains true. If you multiply each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remain true.

Subtraction Property of Inequality

If you subtract the same number from each side of an inequality, the inequality remains true.

Inverse Operations

Operations that "undo" each other, such as addition and subtraction or multiplication and division.

Evaluate

Substitute a number for each variable in an algebraic expression. Then use the order of operations to find the value of the numerical expression.

Like Terms

Terms of an algebraic expression that have the same variables raised to the same exponents. Examples: 4 and 8, 2x and 7x.

Order of Operations

The order in which to perform operations when evaluating expressions with more than one operation. For example, to evaluate 5+2×3 you perform the multiplication before the addition.

Terms

The parts of an expression that are added together. The terms 4x+7 are 4x and 7.

Addition Property of Inequality

The sum of an integer and its additive inverse is zero. 8+(-8)=0.

Distributive Property

To multiply a sum or difference by a number, multiply each number in the sum or difference by the number outside the parentheses.

Simplify (an expression)

To remove brackets, unnecessary terms, and numbers.