Transcript Welcome to the Unit 2 Seminar for College Algebra!

MM212 Unit 2 Seminar Agenda
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Combining Like Terms
Evaluating Algebraic Expressions
Grouping Symbols
Addition Properties
Multiplication Properties
Solving Equations
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
• 3x2 + 5x2 = 8x2
• 3x + 5y …. Does not combine … not like terms
• 3x2 + 5y2 …. Does not combine … not like terms
• 3x2 + 5x3 …. Does not combine … not like terms
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
Geometry Review
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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
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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
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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.
Grouping Symbols
Remember to work from the inside – out
Examples:
2[4-3(5-2)]
-3{2x-3[x+4(x-1)]}
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
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
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.
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.
Solving Equations:
Solve the following equations for x:
1. x + 2 = 5
2. -6 = x - 4
Solving Equations
Solve the following equations for a:
1. 5a = 15
2. -36 = 9a
Solving Equations
Solve the following equations for y:
1. 4y – 5 = 7
2. -6y + 2 = -11
Solving Equations
Solve the following equations for b:
1. 5(b-3) + 1 = -2
2. 7(b-3) = -2(1-b)
Questions?