Algebraic Expressions Eq N… · algebraic expression Ex: Solving Equations.notebook 5 October 01,...
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Solving Equations.notebook 1 October 01, 2014 Algebraic Expressions
Transcript of Algebraic Expressions Eq N… · algebraic expression Ex: Solving Equations.notebook 5 October 01,...
Solving Equations.notebook
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October 01, 2014
Algebraic Expressions
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Warm-up: Fill-in the blank.
The product is the answer to a _____________ problem.
The quotient is the answer to a _____________ problem.
The difference is the answer to a _____________ problem.
The sum is the answer to a _____________ problem.
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Addition
What words or phrases can be used to represent the operations?
Multiplication
Subtraction
Division
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Evaluating Algebraic Expressions
variable - a letter or symbol that represents an unknown valueEx:
substitution - replacing a variable with a valueEx:
term - part of an algebraic expression that can be a number, a variable, or a product of bothEx: In the expression 2x + 14 the terms are 2x and 14
coefficient - the numerical factor in the term of an algebraic expressionEx:
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Simplifying Algebraic Expressions
like terms - terms that have the same variables with the same corresponding exponents Ex: In the expression 2x + 4 + x + 1, the terms 2x and x are like terms, as are 4 and 1
equivalent expressions - expressions that are equal for all values of the variable Ex:
simplify - to write an equivalent expression by combining like terms Ex:
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Mathematical Properties
commutative property - a + b = b + a
associative property - (a + b) = c = a + (b + c)
distributive property - a (b + c) = (a b) + (a c)
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Solving Equations
When solving equations, the objective is to get the variable on one side of the equation and everything else on the other. In order to do this, you must "undo" the equation. Undoing an equation means that you perform opposite operations. Addition and Subtraction are opposite operations. Multiplication and Division are also opposites.
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ex. 1: x + 1 = 5 ex. 2: x 4 = 15
ex. 3: 12 x = 8 ex. 4: 20 = 14 x
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ex. 5: 4x = 12 ex. 6: = 12
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ex. 7: ex. 8:
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MultiStep Equations
ex. 9: ex. 10:
Write these problems down!
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ex. 11: 0.8z + 3.74 = z + 1.5
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ex. 12: 4y 1 = 2(y 2)
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A.REI.3: Solve linear equations in one variable, including equations with coefficients represented by letters.
2.2. Solving Equations in One Variable• Some equations may have no solution. For example, when solving results in something impossible, like 2 = 6.
Solve the equation 2(3x + 1) = 6x + 14.
• Some equations will have infinitely many solutions. For example, when solving results in the same value on each side of the equal sign, such as 2x = 2x.
Solve the equation 3(4x + 2) = 12x + 6.
• Other equations will only have one solution. For example, when solving results in the variable equal to a number, such as x = 5.
Solve the equation 5x + 9 = 2x – 36.
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ex. 13: Does this equation have one solution, no solutions, or infinitely many solutions?
10q 15 = 5(2q + 4)
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Worktime: Solving Equations
1. 14 – 3y = 4y 2. r – 4 + 6r = 3 + 8r
3. 6(2x – 4) = 3(4x + 8) 4. 2(8x + 10) = 4(4x + 5)
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1. There are 24 cookies on a plate. Jenna and Torri eat n cookies each. How many cookies are left?
A. 2n
B. 12n
C. 24 + 2n
D. 24 2n
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2. 14 minus a number
One less than a number y
Sum of four and a number b
A number y divided by 40
n students organized into seven equal teams
Six more than three times a number m
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3. The number of stamps in Ethan's collection is 4 more than half the number of stamps in Helen's collection.
h + 42
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4. The number of pledges that Melissa collected for this year's charity walk is 8 less than half the number of pledges she collected last year. She collected p pledges last year. Which expression represents the number of pledges she collected this year?
A. 2p 8 C. p 8
B. p 8p
D. 8 p
2
2
2
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5. Diego has 60 CDs. This is 12 more CDs than Heidi has. How many CDs does Heidi have?
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6. Simon has six less than 2/3 of the number of baseball cards that Manuel has. Simon has 14 baseball cards. How many cards does Manuel have?
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7. A taxi charges $2.50 for each ride plus $1.25 per mile traveled. If the total charge for one ride was $8.75, how many miles were traveled?
