Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015

Jag Mark:

Lesson 2.1 - Solving One - Step Equations

ex 1) x + 3 = 2

Addition Property of Equality: Adding the same number to each side of an equation produces an equivalent equation.

Subtraction Property of Equality: Subtracting the same number from each side of an equation produces an equivalent equation.ex 2) x + 3 = 2

ex 3) y + 2 = -6 ex 4) -7 = b - 3Identify the property used to solve each equation below.

Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015

Multiplication Property of Equality: Multiplying the same number by each side of an equation produces an equivalent equation.

Multiplication and Division Properties of Equality

is equivalent to

Division Property of Equality: Dividing each side of an equation by the same nonzero number produces an equivalent expression.

is equivalent to

Identify the property used to solve each equation below.

1. 10 = 15x 2.

x= 2

3x 33

= 2 3

5x = 205x = 205 5

x-9

=8

3) 4x = 6.4

5) 6) 5y = 24

Solve each equation using the appropriate property of equality.

4)

12

- y =35

Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015

Lesson 3.1-3.3 Solving Inequalities

Each of the properties of equalities that we discussed also apply to inequalities.

1) Addition Property of Inequality

2) Subtraction Property of Inequality

3) Division Property of Inequality

4) Multiplication Property of Inequality***However...if you are using the multiplication/division property of inequality with a negative number, the inequality sign must reverse.

Use the appropriate properties to justify the solution of each inequality. (Remember that negative numbers can impact your inequality sign.)

1) 2)

3) 4)

Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015Lesson 2.2 and 3.4 - Solving Two - Step Equations and Inequalities

ex 1) 2x + 3 = 15

ex 2)

ex 4)ex 3)

Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015

ex 5) ex 6)

ex 7) ex 8)

Lesson 2.3 and Lesson 3.4 - Solving Multi - Step Equations and Inequalities:

Combining Like Terms:

ex 1) 5 = 5m - 23 + 2m

ex 2)

Martha takes her niece and nephew to a concert. She buys T-shirts and bumper stickers for them. The bumper stickers cost $1 each. Martha's niece wants 1 shirt and 4 bumper stickers, and her nephew wants 2 shirts but no bumper stickers. If Martha can spend no more than $67, what is the cost of one shirt?

Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015

Solving an equation using the Distributive Property (Clearing Parentheses):

ex 3) -8(2x - 1) = 36

Solving an equation that contains fractions (Clearing Fractions):

ex 4)

Solving an equation that contains decimals (Clearing Decimals):ex 5) 3.5 - 0.02x = 1.24

ex 6) ex 7)Extra Practice:

-2(3x + 9) < 24

Woodard Solving Equations and Inequalities Notes (Algebra)

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August 28, 2015

Homework:

Lesson 2.2 page 91 #'s 11 - 23 odd

Lesson 2.3 page 98 #'s 11 - 19 odd

Lesson 3.1 page 168 #'s 9, 11

Lesson 3.2 page 174 #'s 9 - 27 odd, 42

Lesson 3.3 page 181 #'s 7 - 11 odd; 19 - 27 odd, 31

Lesson 3.4 page 190 #'s 17 - 43 odd, 45