Expressions and Equations

A symbol or letter that represents one or more numbers. - Normally a letter

A number multiplied by a variable or product of variables - a number next to a variable

constants A number on its own in an expression or equation. Example Definition constants Characteristics Non-Example - A number

A mathematical phrase that can have a contain numbers, variables, and operators. Does not have an equal sign Contains +, -, x, and/or ÷

Algebraic Expressions Examples:

To solve algebraic equations, you need to isolate the variable. Perform the inverse operation. The inverse of addition is subtraction. The inverse of subtraction is addition. The inverse of division is multiplication. The inverse of multiplication is division. Remember: whatever you do to one side, you must do to the other!

The product of a number and a sum is the same as the product of individual addends and the number. Has both multiplication and addition or subtraction Has paratheses

Two or more terms that have the same variables raised to the same powers. The variables in a term must be the same The exponents with the variables must be the same

3, 24, -1/2, 0.75 3 & -9y 24 & 7a² 2x & 3x, 4y & -9y, 7a² & 2a² 2a² & 2x 2x+3x = 5x, 4y-9y=-5y, 7a² + 2a² = 9a² 5a³ & 9a² Constants with constants Same variable with same exponent Add or subtract the coefficients Cannot combine constants with variables and different exponents

Examples: 4a – 3b + 7a 16b – 4x + 3b + 14x -4m + 8b – 4c + 13c (4a + 3b + 8r)- (3a + 10b + 6r) (15g + 4b) + (11g + 13b) + (8g + 13b)

Distributive Property Find the sum. -2x + 3x Look for common factors. X Rewrite the expression. (-2 · x) + (3 · x) Take out the common factor. X(-2 + 3) Simplify. -2 +3 = 1 x(1) = x -2x + 3x = x Find the sum. ( 2 3 x + - 3 7 x) + 3 7 Use the number properties. Associative ( - 3 7 x + 3 7 x) = 0 Simplify. Additive Inverses and Identity Property 2 3 x + 0 = 2 3 x ( 2 3 x + - 3 7 x) + 3 7 = 2 3 x

Distributive Property Factor each expression completely. 12n – Look for the GCF (variables too!) n Use the distributive property. (12 · n) – ( 3 8 m · n) Take out the GCF and put in front of the ( ). n( ) The rest goes inside the ( ). n(12 - 3 8 m ) 3 8 mn

Two-Step Equations 3x + 15 = 18 1. Get rid of the constant by using the inverse of addition or subtraction. 16 – 4x = 64 2. Isolate the variable by using the inverse of multiplication or division. 3(4m – 5) = -19 *Check your answer! 5𝑥 2 = 10

Solving Inequalities Solve inequalities just like you would solve an equation. BUT…… *When multiplying or dividing inequalities with a negative number, you need to FLIP the sign! 1. Isolate the variable and divide by the factor. *Do not forget the negative!* 1. Divide by the inverse. 2. Reverse the inequality sign. 2. Flip the inequality sign. -40x > -30 −𝑥 3 > 8 By a negative number Dividing both sides By a negative number Multiplying both sides

Graphing Inequalities 𝑠 3 >3 f + 7 < 2 open V – 8 ≥ 1 𝑝 2 ≤3 closed *The direction of the graph will be the same as your final answer of your inequality sign. −𝑥 3 >8