1. 3-3 HW: Pg. 150-153 #4-16eoe, 18-28e, 38, 44-45

3. 44. B 45. A

4. Quiz 1 Pg. 153 #1-13

6. Wir2.5 LESSON

8. 3-4 Solving Equations with Variables On Both Sides Still use the ___________________________! Steps for Solving Linear Equations: 1.) Use the _________________to remove any grouping symbols. 2.) Simplify the expression _______________________. 3.) Use properties of equality to collect the _______ terms on one side of the equation and the _______ terms on the other side of the equation. 4.) Use properties of equality to ____________________. 5.) ______ your solution in the original equation. Linear equations do not always have one solution. If variables cancel and you get a _______ statement, there is __________! An ________ is an equation that is ______ for all values of the variable. If variables cancel and you get a ________ statement, there are an infinite number of answers. OPPOSITE OPERATION distributive property on each side of the equation variable constant solve for the variable Check no solution identity FALSE TRUE

9. Animated Activity classzone.com Solve Equations with Variables on Both Sidesolve Equations with Variables on Both Sides

10. EXAMPLE 1 Solve an equation with variables on both sides + 8x + 8x 7 = 12x – 17 24 = 12x Add 8x to each side. Simplify each side. Add 17 to each side. Divide each side by 12. ANSWERThe solution is 2. Check by substituting 2 for x in the original equation. Solve 7 – 8x = 4x – 17. 2 = x 12 12 +17 + 17 Write original equation. Substitute 2 for x. Simplify left side Simplify right side. Solution checks. –9 = 4(2) – 17 ? 7 – 8(2) = 4(2) – 17 ? 7 – 8x = 4x – 17 CHECK –9 = –9

11. EXAMPLE 2 Solve an equation with grouping symbols 9x – 5 = 4x + 15 5x – 5 = 15 5x = 20 x = 4 Distributive property Subtract 4x from each side. Add 5 to each side. Divide each side by 5. 9x – 5 =9x – 5 = 1 4 (16x + 60). Solve -4x -4x +5 +5 5 5

12. GUIDED PRACTICE for Examples 1 and 2 3 ANSWER1. 24 – 3m = 5m Solve the equation. Check your solution. 2. 20 + c = 4c – 7 ANSWER 9 3. 9 – 3k = 17k – 2k ANSWER –8 4. 5z – 2 = 2(3z – 4) ANSWER 6 5. 3 – 4a = 5(a – 3) ANSWER 2 8y – 6 =8y – 6 = 2 3 (6y + 15) 6.6. ANSWER 4

13. Solve a real-world problem EXAMPLE 3 CAR SALES A car dealership sold 78 new cars & 67 used cars this year. The number of new cars sold by the dealership has been increasing by 6 cars each year. The number of used cars sold by the dealership has been decreasing by 4 cars each year. If these trends continue, in how many years will the number of new cars sold be twice the number of used cars sold ? SOLUTION Let x represent the number of years from now. So, 6x represents the increase in the number of new cars sold over x years and –4x represents the decrease in the number of used cars sold over x years. Write a verbal model. 6778 + 6x6x = 2 ( + (– 4 x) )

14. Solve a real-world problem EXAMPLE 3 78 + 6x = 2(67 – 4x) 78 + 6x = 134 – 8x 78 + 14x = 134 14x = 56 x = 4 Write equation. Distributive property Add 8x to each side. Subtract 78 from each side. Divide each side by 14. ANSWER The number of new cars sold will be twice the number of used cars sold in 4 years. 14 14 +8x +8x -78 CHECK You can use a table to check your answer. YEAR 0 1 2 3 4 Used car sold 6763 59 55 51 New car sold 7884 9096102

15. GUIDED PRACTICE for Example 3 7. WHAT IF? In Example 3, suppose the car dealership sold 50 new cars this year instead of 78. In how many years will the number of new cars sold be twice the number of used cars sold? ANSWER 6 yr

16. SOLUTION EXAMPLE 4 Identify the number of solutions of an equation Solve the equation, if possible. a. 3x = 3(x + 4) b. 2x + 10 = 2(x + 5) a. 3x = 3x + 12 Distributive property -3x -3x FALSE statement ANSWER a. The statement 0 = 12 is not true, so the equation has no solution. Subtract 3x from each side. 10 = 10 b. 2x + 10 = 2x + 10 Distributive property -2x Subtract 2x from each side. 0 = 12 TRUE statement b. The statement 1 0 = 10 is true, so the equation is an identity.

17. GUIDED PRACTICE for Example 4 8. 9z + 12 = 9(z + 3) Solve the equation, if possible. ANSWER no solution 9. 7w + 1 = 8w + 1 ANSWER 0 10. 3(2a + 2) = 2(3a + 3) ANSWER identity

18. Summary Is the equation -2(4-x)=2x-8 an identity? Explain why or why not. Ans: Yes, it is an identity because it is true for all values of x since the left side equals the right side. Decide if the state is true or false. The solution of x=2x is zero. Ans: True Solve 9(9-x)=4x-10. Explain each step along the way.

19. Check Yourself Pg. 157-159 #4-24e, 2844eoe, 49-50, 56-57