Expressions and Equations Targets: 1) Write & evaluate algebraic expressions. 2) Determine if a # is a solution of an equation.

Warm-Up

VOCAB Variable: Algebraic expression: Evaluate: Equation: Solution: A letter that represents one or more numbers. Algebraic expression: contains numbers, operations, and variables Does NOT have = 2N + 3 Evaluate: Find the value Equation: 2N + 3 = 5 Solution: An answer that makes an equation true.

Evaluating an Expression Rewrite the expression by substituting the given value(s) for the variable(s). Follow the order of operations to find the value of the expression.

Example 1a Evaluate the algebraic expression. 5N – 3 when N = 8 Substitute 8 for N 5(8) – 3 Multiply. 40 – 3 Subtract. 37

Example 1b Evaluate the algebraic expression. (y + 2)2 + p when y = –7 and p = 9 Substitute –7 for y and 9 for p. (–7 + 2)2 + (9) Add inside the parentheses. (–5)2 + 9 Square. 25 + 9 Add. 34

Example 2 Write an algebraic expression for each phrase. The product of seven and m 7m Two less than six times x 2 + 6x or 6x + 2 Y divided by three then decreased by four

Example 3a Determine if the number given is the solution of the equation. –2y + 6 = –16 Is 5 the solution? Substitute 5 for y. –2(5) + 6 ≟ –16 Multiply. –10 + 6 ≟ –16 Add. – 4 ≠ –16 Five is not the solution.

Example 3b Determine if the number given is the solution of the equation. Is 40 the solution? Substitute 40 for x. Divide. Subtract. Forty is the solution. ≟ 4 ≟ 4

Exit Problems Evaluate when x = 24 Write an algebraic expression for the phrase “seven less than x” Determine if 3 is the solution to the equation 1 – 2x = 7

Communication Prompt Why are variables used in mathematics?