1. MTH 10905 Algebra THE ADDITION PROPERTY OF EQUALITY CHAPTER 2 SECTION 2

2. Equations are statements that show two algebraic expressions are equal  2x + 1 = x – 5 is an example of an equation Linear Equation in one variable is an equation that can be written in the form ax + b = c a, b and c are real numbers and c ≠ 0 Linear Equations in other words is an equation which has 1 variable that is multiplied by a number and some constant. It can also have the variable on both sides of the equation. For example: x + 4 = 2x – 6 Identify Linear Equations

3. Examples of Linear Equations: Exp:4x – 3 = 5 Exp:x + 1 = -6 Exp:x + 5 = 5x + 2 Exp:x + 9 = 52 Exp:27 = x + 16 Identify Linear Equations

4. Solve an Equations is to find the number that when substituted for the variable makes the equation true. Checked is when we substitute the answer that is believed to be the answer into the original equation. We use a when we are checking to see if this is a true statement. When solving or checking keep your equal signs in line to help you follow your work. Identify Linear Equations

5. Exp: Consider the equation 6x – 5 = 25 is 3 a solution No, 3 is not a solution Linear Equations

6. Exp: Determine whether 35 is a solution to the equation 4x – 3(x – 5) = 50 Yes, 35 is a solution Linear Equations

7. Exp: Determine whether is a solution to the equation 4(x+ 3) = 7 + x LCD = 3 Yes, is a solution Linear Equations

8. Identify Equivalent Equations Solve an Equation to solve an equation you have to get the variable alone on one side of the equal sign or isolate the variable. Equation must be in the form of x = some number To ensure that an equation remains equal or balanced we have to do the same thing to both sides of the equation. If I have a balanced scale and I add 3 lbs to one side what do I have to do to keep it balanced? Adding, subtracting, multiplying or dividing a number to the left side means to add, subtract, multiply or divide the same number to the right side.

9. Addition Property of Equality Equivalent equations are two or more equations with the same solution. Exp: 3x + 3 = 6 and 3x = 3 equivalent because the solution to both is 1 To solve an equation we can use the addition property of equality or the multiplication property of equality The addition property says if a = b then a + c = b + c for any real number a, b, and c The addition property of equality is used to make an equivalent equation and when used correctly t can be used to solve an equation

10. Addition Property of Equality The multiplication property says if a = b then a · c = b · c for any real number a, b, and c Addition property is used to solve equation in the form of x + a = b When we add or subtract to the left side we must add or subtract to the right side to keep the equation equal. This eliminates the number on the same side of the equal sign as the variable. Subtraction is defined in terms of addition, therefore the addition property allows us to also subtract on both sides of an equation

11. Addition Property of Equality Exp: x + 3 = 10CHECK: x + 3 = 10 x + 3 – 3 = 10 – 3 7 + 3 = 10 x = 7 10 = 10 Exp:x – 4 = 5CHECK:x – 4 = 5 x – 4 + 4 = 5 + 49 – 4 = 5 x = 9 5 = 5

12. Addition Property of Equality Exp: a – 8 = -12CHECK: a – 8 = -12 a + 8 – 8 = -12 + 8 -4 – 8 = -12 x = -4 -12 = -12 Exp:t + 4 = 7CHECK:t + 4 = 7 t – 4 + 4 = 7 – 4 3 + 4 = 7 t = 3 7 = 7

13. Addition Property of Equality Exp: -5 = b + 10CHECK: -5 = b + 10 -5 – 10 = b + 10 – 10 -5 = -15 + 10 -15 = b-5 = -5 Remember that our goal is to isolate the variable on one side of the equation. To do this we add or subtract the number on the same side as the variable to both sides of the equation. Exp: -10 = x – 3CHECK: -10 = x – 3 -10 + 3 = x-10 = -7 – 3 -7 = x-10 = -10

14. Addition Property of Equality Exp: -8.75 = r + 13.25 -8.75 – 13.25 = r + 13.25 – 13.25 -22.00 = r CHECK: -8.75 = r + 13.25 -8.75 = -22.00 + 13.25 -8.75 = -8.75

15. HOMEWORK 2.2 Page 111 – 112 #25, 29, 33, 53, 57, 67