Unit 2 Solve Equations and Systems of Equations Algebraic Properties to Solve Equations

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.

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.

Name the property used in each example. Inverse Prop. of Addition 5 + -5 = 0 -3 + 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

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

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

Associative Properties Associative Property of Addition Associative Property of Multiplication

Name the property used in each example. -7 + (-3 + 4) = (-7 + -3) + 4 3 + -4 = -4 + 3 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

Name the property used in each example. x(yz) = (xy)z 3x + 5y + -7 = -7 + 3x + 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

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.

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

Solve for x. Write the logical steps in the solution to each equation. 1) m + 2 = 10 -2 -2 Subtraction Prop. of Equality m = 8 2) x - 4 = 6 +4 +4 Addition Prop. of Equality x = 10

Solve for x. Write the logical steps in the solution to each equation. Division Prop. of Equality 5 5 x = 7 4) (-6) (-6) Multiplication Prop. of Equality -72 = x

Solve for x. Write the logical steps in the solution to each equation. Subtraction Prop. of Equality -3 -3 2x = 8 Division Prop. of Equality 2 2 x = 4

Solve for x. Write the logical steps in the solution to each equation. +4 +4 Addition Prop. of Equality (3) (3) Multiplication Prop. of Equality x = 18

Solve for x. Write the logical steps in the solution to each equation. Distributive Prop. 3x - 6 = 17 +6 +6 Addition Prop. of Equality 3x = 23 Division Prop. of Equality 3 3

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.

Solve for x. Write the logical steps in the solution to each equation. -6 -6 Subtraction Prop. of Equality (-5) (-5) Multiplication Prop. of Equality -35 = x x = -35 Symmetric Prop. of Equality

Name the property used in each example. If x = 4, then x + 7 = 4 + 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.

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.