1 Solving Linear Equations

2 Like Terms Like terms contain the same variables raised to the same powers. To combine like terms, add or subtract the numerical coefficients (as appropriate), then multiply the result by the common variable factors. You can combine like terms by adding or subtracting them (this is not true for unlike terms).

3 Combining Like Terms 6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2 – 11xy Can’t be combined (since the terms are not like terms) Examples of Combining Terms Terms Before CombiningAfter Combining Terms

4 Combining Like Terms We cannot combine a chicken and a goat and create a Chickengoat It would be unbalanced!!!

5 Combining Like Terms Or a Zonkey???

6 Using the Distributive Property a.) 2(x + y) = 2x + 2y Example: Find each product by using the distributive property to remove the parentheses. b.) 7(x + 2y – 5z) = 7x + 14y – 35z c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c a.) 2(x + y) b.) 7(x + 2y – 5z)c.) – 4(3a – 3b – 10c)

7 Remember to keep it balanced by distributing to everyone Using the Distributive Property

8 Addition Property of Equality If a, b, and c are real numbers, then a = b and a + c = b + c are equivalent equations. Addition Property of Equality z = – 16 Simplify both sides. Example: 8 + (– 8) + z = – 8 + – 8 Add –8 to each side. 8 + z = – 8 a.) Keep it balanced

9 Example: Solving Equations 5(3 + z) – (8z + 9) = – 4z z – 8z – 9 = – 4z Use distributive property. 6 – 3z = – 4z Simplify left side. 6 + z = 0 Simplify both sides. z = – 6 Simplify both sides. 6 – 3z + 4z = – 4z + 4z Add 4z to both sides. 6 + (– 6) + z = 0 +( – 6)Add –6 to both sides.

10 Multiplication Property of Equality If a, b, and c are real numbers, then a = b and ac = bc are equivalent equations Multiplication Property of Equality Example: – y = 8 y = – 8Simplify both sides. ( – 1)( – y) = 8( – 1) Multiply both sides by –1. Balanced

11 Divide both sides by 3. Example: Using Both Properties 3z – 1 = 26 3z = 27 Simplify both sides. z = 9 Simplify both sides. 3z – = Add 1 to both sides.

12 Solving Linear Equations Solving Linear Equations in One Variable 1)Multiply both sides by the LCD to clear the equation of fractions if they occur. 2)Use the distributive property to remove parentheses if they occur. 3)Simplify each side of the equation by combining all like terms. 4)Get all variable terms on one side and all numbers on the other side by using the addition property of equality. 5)Get the variable alone by using the multiplication property of equality. 6)Check the solution by substituting it into original equation.