1. MM212 Unit 2 Seminar Agenda Combining Like Terms Evaluating Algebraic Expressions Grouping Symbols Addition Properties Multiplication Properties Solving Equations

2. COMBINING LIKE TERMS Like terms are combined by adding or subtracting the numerical coefficients AND keeping the SAME variables with the SAME exponents EXAMPLES: 3 oranges + 5 oranges = 8 oranges 3x + 5x = 8x 3x 2 + 5x 2 = 8x 2 3x + 5y …. Does not combine … not like terms 3x 2 + 5y 2 …. Does not combine … not like terms 3x 2 + 5x 3 …. Does not combine … not like terms

3. Evaluating Algebraic Expressions Substitution: When you replace the variable with a number Examples: Evaluate 4x + 2 if x = 5 4(5)+2 = 22 Evaluate a^2 – a +1 if a = -2

4. Geometry Review Perimeter is the distance around a closed figure Example: The sides of a triangle have lengths of 3 meters, 7 meters, and 4 meters. Determine the perimeter. P = s1 + s2 + s3 P = 3 + 7 + 4 = 14 Therefore, the perimeter is 14 meters Area is the measurement of surface measured in square units Example: Find the area of a rectangular yard enclosed by a fence 12 yards long and 8 yards wide. A = lw A = (12)(8) A = 96 Therefore, the area is 96 square yards Volume is space within a figure measured in cubed units Example: Find the volume of a rectangular solid with length 10 feet, width 6 feet and height 4 feet. V = LWH V = (10)(6)(4) V = 240 Therefore, the volume is 240 cubic feet.

5. Grouping Symbols Remember to work from the inside – out Examples: 2[4-3(5-2)] -3{2x-3[x+4(x-1)]}

6. Properties of Addition Commutative Property of Addition Changes order a + b = b + a Associative Property of Addition Changes grouping (a + b) + c = a + (b + c) Identity Property of Zero Anything added to 0 is itself a + 0 = a and 0 + a = a Inverse Property of Addition Anything plus its opposite is 0 a + (-a) = 0 and –a + a = 0

7. Properties of Multiplication Commutative Property of Multiplication Changes order a * b = b * a Associative Property of Multiplication Changes grouping (a * b) * c = a * (b * c) Identity Property of 1 Anything times 1 is itself a * 1 = a and 1 * a = a Inverse Property of Multiplication Anything times its reciprocal is 1 a * 1/a = 1 and 1/a * a = 1

8. Properties of Equality Addition/Subtraction Property of Equality you can add or subtract the same number from both sides of the equation and the equation is still true If a = b, then a+c = b+c. Multiplication/Division Property of Equality You can multiply or divide the same number on both sides of the equation and the equation is still true If a = b, then ac = bc.

9. Steps For Solving Equations STEP1: Clear the grouping symbols using the distributive property. STEP2:Clear the fractions by multiplying EVERY term by a common denominator (it does NOT have to be the least common denominator). STEP3: Move all the variables to one side of the equal symbol using the addition or subtraction property of equality. STEP4: Move all the plain numbers to the other side of the equal symbol using the addition or subtraction property of equality. STEP5: Isolate the variable using the multiplication or division property of equality. STEP6: Substitute your solution into the ORIGINAL equation to see if a true statement results.

10. Solving Equations: Solve the following equations for x: 1. x + 2 = 52. -6 = x - 4

11. Solving Equations Solve the following equations for a: 1. 5a = 152. -36 = 9a

12. Solving Equations Solve the following equations for y: 1. 4y – 5 = 72. -6y + 2 = -11

13. Solving Equations Solve the following equations for b: 1. 5(b-3) + 1 = -2 2. 7(b-3) = -2(1-b)

14. Questions?