Do Now Evaluate. 1. 5(7) – 1 2. 7(18 – 11) 3. 22 + 17  8 + 3 34 4. 36 + 15(40 – 35) 5. 33 + 7(12 – 4) 34 49 161 111 83 HWK; p 7 and p 10

EQ: How do I evaluate and simplify algebraic expressions? M7A1b Evaluate algebriac expressions, using commuative, associative, and distributive properties

Vocabulary Variable – a letter that represents a number Constant – a number algebraic expression – consist of one or more variables Evaluate – substitute a number for a variable

Additional Example 1: Evaluating Algebraic Expressions Evaluate k + 9 for each value of k. A. k = 5 k + 9 5 + 9 Substitute 5 for k. 14 Add. B. k = 2 k + 9 2 + 9 Substitute 2 for k. 11 Add.

Check It Out: Example 1 Evaluate a + 6 for each value of a. A. a = 3 9 Add. B. a = 5 11 Add.

Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.

Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations Evaluate the expression for the given value of the variable. A. 4x – 3 for x = 2 4(2) – 3 Substitute 2 for x. Multiply. 8 – 3 5 Subtract.

Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 18 C. 5x2 + 3x, for x = 2 26

Check It Out: Example 2A Evaluate the expression for the given value of the variable. A. 3x – 2 for x = 3 7

Check It Out: Example 2 B. r ÷ 3 + r, for r = 12 16 C. 4y2 + 2y, for y = 3 42

Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6 a Evaluate + 4b, for a = 3 and b = 2. 10

Check It Out: Example 3 8 w Evaluate + 2x, for w = 4 and x = 2. 6

 Equations and Their Solutions 1-10 Course 2 1-10 Equations and Their Solutions Additional Example 1A: Determining Whether a Number is a Solution of an Equation Determine whether the given value of the variable is a solution of t + 9 = 17. 26 t + 9 = 17 26 + 9 = 17 ? Substitute 26 for t. 35 = 17 ?  26 is not a solution of t + 9 = 17.

 Equations and Their Solutions 1-10 Course 2 1-10 Equations and Their Solutions Additional Example 1B: Determining Whether a Number is a Solution of an Equation Determine whether the given value of the variable is a solution of t + 9 = 17. 8 t + 9 = 17 8 + 9 = 17 ? Substitute 8 for t. 17 = 17 ?  8 is a solution of t + 9 = 17.

Insert Lesson Title Here Course 2 1-10 Equations and Their Solutions Insert Lesson Title Here Check It Out: Example 1 Determine whether each number is a solution of x – 5 = 12. A. 22 x – 5 = 12 22 – 5 = 12 ? Substitute 22 for x. 17 = 12 ?  22 is not a solution of x – 5 = 12. B. 8 x – 5 = 12 8 – 5 = 12 ? Substitute 8 for x. 3 = 12 ?  8 is not a solution of x – 5 = 12.

Evaluate n + 7 for each value of n. 1. n = 25 2. n =31 TOTD Evaluate n + 7 for each value of n. 1. n = 25 2. n =31 Evaluate each algebraic expression for the given value of the variables 3. 6y – 5 for y = 7 4. 4x2 + 3x for x = 6 5. + 3y for x = 4 and y = 3 6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? 32 38 37 162 56 x 23 84

Equations and Their Solutions Insert Lesson Title Here Course 2 1-10 Equations and Their Solutions Insert Lesson Title Here TOTD Determine whether the given value of the variable is a solution of 5 + x = 47. 1. x = 42 2. x = 52 Determine whether the given value of the variable is a solution of 57 – y = 18. 3. y = 75 4. y = 39 5. Kwan has 14 marbles. This is 7 more than Drue has. Does Drue have 21 or 7 marbles? yes no no yes 7