Patterns and Algebra L1: Evaluating Algebraic Expressions and Equations L2: Solving Algebraic Expressions

Equations and Expressions Equation Equation An equation has an equal sign making the expression equal to a specific number. An equation has an equal sign making the expression equal to a specific number. Example Example 2a +3b a= 5 b= 9 Expression Expression Determine a numerical value for that expression Determine a numerical value for that expression Always follow the order of operations Always follow the order of operations Example Example X + 7 = 15

Example 1 2a + 3b a= 5 b= 9 Substitute the values for a and b Substitute the values for a and b 2 (5) + 3 (9) = 37

Example 2 Evaluate the expression 2x² - 4x + 9 when x =6 Plug in 6 wherever you see x. Plug in 6 wherever you see x. 2(6)² - 4x = =57

Example 3 Pens cost $.50 and pencils cost $.30. Given the equation C= $.50 + $.30y where C= cost, x= pens, and y= pencils, calculate the cost of buying 7 pens and 9 pencils Pens cost $.50 and pencils cost $.30. Given the equation C= $.50 + $.30y where C= cost, x= pens, and y= pencils, calculate the cost of buying 7 pens and 9 pencils C= $.50 + $.30y C=$.50 (7) + $.30 (9) C= $ $2.70 C=$6.20

Extended Constructed Response On a recent math quiz, the seventh grade students in Mrs. Lopez class were asked to evaluate the expression 4r + 3s – 2t when r = 6, s = 4, and t = 3. Paulina evaluated the expression and determined its value to be 57. On a recent math quiz, the seventh grade students in Mrs. Lopez class were asked to evaluate the expression 4r + 3s – 2t when r = 6, s = 4, and t = 3. Paulina evaluated the expression and determined its value to be 57. Is she correct or incorrect? Is she correct or incorrect? If Paulina’s response is correct show the work proving her answer is correct. If Paulina’s response is correct show the work proving her answer is correct. However, if you believe that Paulina’s response is incorrect, determine what she did incorrectly and show the correct way to evaluate the expression. However, if you believe that Paulina’s response is incorrect, determine what she did incorrectly and show the correct way to evaluate the expression.

Solving Algebraic Equations Four Steps for Solving Equations 1. Isolate Identify the variable by putting a box around it Identify the variable by putting a box around it 2. Inverse Use the inverse operation to get the variable by itself Use the inverse operation to get the variable by itself 3. Solve Do the math! You may have to work backwards in order to get an answer. Do the math! You may have to work backwards in order to get an answer. 4. Check Plug your answer into the original equation. Plug your answer into the original equation.

Example 1 X + 19 = X = = 45 45= 45

Example 2 9X = X= 16 9(16) = =144

Example 3 3x – 21 = X= X= 28 3 (28) – 21 = = 63 63=63