1-4 Solving Equations Properties of Equality Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution

Properties of Equality Reflexive Property a + b = a + b The same expression is written on both sides of the equal sign.

Properties of Equality Symmetric Property If a = b then b = a If 4 + 5 = 9 then 9 = 4 + 5

Properties of Equality Transitive Property If a = b and b = c then a = c If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5

Additional Properties of Real Numbers Substitution Property If a = b, then a can be replaced by b. a(3 + 2) = a(5)

Distributive Substitution Reflexive Symmetric Commutative Transitive Name the property 5(4 + 6) = 20 + 30 5(4 + 6) = 5(10) 5(4 + 6) = 5(4 + 6) If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6) 5(4 + 6) = 5(6 + 4) If 5(10) = 5(4 + 6) and 5(4 + 6) = 20 + 30 then 5(10) = 20 + 30 Distributive Substitution Reflexive Symmetric Commutative Transitive

More Properties of Equality If the operation done to one side is also done to the other then the value of the equation does not change Definition Examples Addition: If a=b, then a + c = b + c Subtraction: If a=b, then a – c = b – c Multiplication: If a=b, then a ∙ c = b ∙ c Division: If a = b, then a / c = b / c (c≠0) If x = 12, then x + 3 = 12 + 3 then x – 3 = 12 – 3 then x ∙ 3 = 12 ∙ 3 If x = 12, then x / 3 = 12 / 3

Solve the Equation Solving an equation that contains a variable means finding all the possible values that make the equation true. The first step is to isolate the variable to one side of the equation by using inverse operations. Inverse operations undo operations. Addition, subtraction are inverse operations as are multiplication, and division .

Example 1 Solve . Check your solution. Original equation Add 5.48 to each side. Simplify. Check: Original equation Substitute 5.5 for s. Simplify. Answer: The solution is 5.5. Example 3-4a

Your turn What is the solution of 12b=18? 12b / 12 = 18 / 12 Divide each side by 12 b = 3 / 2 Simplify

Distributive and Substitution Properties Solve Original equation Distributive and Substitution Properties Commutative, Distributive, and Substitution Properties Addition and Substitution Properties Division and Substitution Properties Answer: The solution is –19. Example 3-5a

Your turn What is the solution of -27 + 6y = 3(y – 3)? -27 + 6y = 3y – 9 Distributive Property 6y = 3y + 18 Add 27 to each side. 3y = 18 Subtract 3y from each side y = 6 Divide each side by 3.

Your turn What is the solution of 3( 2x – 1) – 2(3x + 4)=11x? 6x – 3 – 6x – 8 = 11x Distributive Property – 11 = 11x Combine Like Terms – 1 = x Divide each side by – 11 x = – 1 Symmetric Property

Your turn Suppose the flower carpet from Problem 3 had a perimeter of 320 meters. What would the dimensions of the flower carpet be?

Problem 4 Page 29

Problem #5 Page 29

Another Literal Equation Distance = Rate x Time or d = r ∙ t Solve for r Solve for t