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Published byGertrude Barrett Modified over 5 years ago

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**Unit 2 Solve Equations and Systems of Equations**

Algebraic Properties to Solve Equations

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**Identity Properties a + 0 = a Identity Property of Addition**

If you add 0 to any number, you will get that number. 0 is sometimes called the additive identity. Identity Property of Multiplication If you multiply 1 by any number, you will get that number. 1 is sometimes called the multiplicative identity.

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**Inverse Properties Inverse Property of Addition**

If you add a number and its opposite, you get 0. Inverse Property of Multiplication If you multiply a number by its reciprocal, you get 1.

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**Name the property used in each example.**

Inverse Prop. of Addition = 0 = -3 5(1) = 5 4(¼) = 1 -3•1 = -3 Identity Prop. of Addition Identity Prop. of Multiplication Inverse Prop. of Multiplication Identity Prop. of Multiplication

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**Name the property used in each example.**

Identity Prop. of Multiplication 1x = x -x + x = 0 3x + 0 = 3x Inverse Prop. of Addition Inverse Prop. of Multiplication Identity Prop. of Addition

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**Commutative Properties**

Commutative Property of Addition You can add numbers in any order. Commutative Property of Multiplication You can multiply numbers in any order.

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**Associative Properties**

Associative Property of Addition Associative Property of Multiplication

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**Name the property used in each example.**

-7 + (-3 + 4) = ( ) + 4 = 5(-2) = -2(5) (4•3)5 = 4(3•5) Associative Prop. of Addition Commutative Prop. of Addition Commutative Prop. of Multiplication Associative Prop. Of Multiplication

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**Name the property used in each example.**

x(yz) = (xy)z 3x + 5y + -7 = x + 5y (3 + 5x) + 4 = 3 + (5x + 4) 3(2y) = (2y)3 (-4 + 7) + 3 = 3 + (-4 + 7) Associative Prop. of Multiplication Commutative Prop. of Addition Associative Prop. of Addition Commutative Prop. of Multiplication Commutative Prop. of Addition

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**Addition Property of Equality**

If a = b, then a + c = b + c. You can add the same number to both sides of an equation. Subtraction Property of Equality If a = b, then a – c = b – c. You can subtract the same number from both sides of an equation.

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**Multiplication Property of Equality**

If a = b, then ac = bc. You can multiply both sides of an equation by the same number. Division Property of Equality If a = b, then You can divide both sides of an equation by any nonzero number. Distributive Property a(b + c) = ab + ac

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**Solve for x. Write the logical steps in the solution to each equation.**

1) m + 2 = 10 Subtraction Prop. of Equality m = 8 2) x - 4 = 6 Addition Prop. of Equality x = 10

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**Solve for x. Write the logical steps in the solution to each equation.**

Division Prop. of Equality x = 7 4) (-6) (-6) Multiplication Prop. of Equality -72 = x

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**Solve for x. Write the logical steps in the solution to each equation.**

Subtraction Prop. of Equality 2x = 8 Division Prop. of Equality 2 2 x = 4

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**Solve for x. Write the logical steps in the solution to each equation.**

Addition Prop. of Equality (3) (3) Multiplication Prop. of Equality x = 18

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**Solve for x. Write the logical steps in the solution to each equation.**

Distributive Prop. 3x - 6 = 17 Addition Prop. of Equality 3x = 23 Division Prop. of Equality

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**Reflexive Property a = a**

Any value equals itself. Symmetric Property If a = b, then b = a. You can “swap” two sides of an equation. Substitution Property If a = b, then a can be substituted for b.

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**Solve for x. Write the logical steps in the solution to each equation.**

Subtraction Prop. of Equality (-5) (-5) Multiplication Prop. of Equality -35 = x x = -35 Symmetric Prop. of Equality

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**Name the property used in each example.**

If x = 4, then x + 7 = If 7 = y, then y = 7. 2 = 2 If x + y = 12, and x = 7, then 7 + y = 12. Substitution Prop. Symmetric Prop. Reflexive Prop. Substitution Prop.

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**Name the property used in each example.**

3 + 2y = 3 + 2y If 9y = 7, then 7 = 9y. If a = 3 and b = 7, then ab = (3)(7). Reflexive Prop. Symmetric Prop. Substitution Prop.

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