1. Objective: To solve equations with variables on both sides. To identify equations that have infinite solutions or no solutions

2.  Solve:  -5x = 30  5x + 15 = 30  2x + 8 – 5 + 3x = 13

3.  7x + 19 = -2x + 55 I want to gather all of my variables on one side of the equal side and all of my numbers on the other side. What should I do first? I usually move my variables to the side that has the most. Which side has the most x’s? + 2x +2x 9x + 19 = 55 Subtract 19 from both sides -19 9x = 36 ÷9 x = 4 Divide both sides by 9 Always check your answer!7(4) + 19 = -2(4) + 55 28 + 19 = -8 + 55 47 = 47 ✓

4.  5x + 2 = 2x + 14 I want to gather all of my variables on one side of the equal side and all of my numbers on the other side. What should I do first? - 2x -2x 3x + 2 = 14 Subtract 2 from both sides -2 - 2 3x = 12 ÷3 x = 4 Divide both sides by 3 Always check your answer!5(4) + 2 = 2(4) + 14 20 + 2 = 8 + 14 22 = 22 ✓ Subtract 2x from both sides

5.  7x + 2 = 4x - 10 I want to gather all of my variables on one side of the equal side and all of my numbers on the other side. What should I do first? - 4x -4x 3x + 2 = -10 Subtract 2 from both sides -2 - 2 3x = -12 ÷3 x = -4 Divide both sides by 3 Always check your answer! 7(-4) + 2 = 4(-4) -10 -28 + 2 = -16 - 10 -26 = -26 ✓ Subtract 4x from both sides Remember…subtractin g is the same as adding the opposite!

6.  90 – 9y = 6y What is different about this? What should I do first? + 9y + 9y 90 = 15y ÷ 15 ÷15 6 = y Divide both sides by 15 Always check your answer! 90 – 9(6) = 6(6) 90 – 54 = 36 36 = 36 ✓ Add 9y to both sides

7.  -3(2x – 5) = 15x + 17 I need to use the Distributive property first. + 6x +6x 15 = 21x+ 17 -17 - 17 - 2 = 21x ÷21 -6x + 15 = 15x + 17 = x This one is just plain ugly! Some of them will be. You just have to work your way through it and remember to check your answer!!!

8.  -4(2x + 4) = -8x + 12 I need to use the Distributive property first. + 8x +8x -16 = 12 -8x + (-16) = -8x + 12 Wait a minute…this doesn’t make any sense????? If you get a situation like this – that just isn’t true…the answer is NO SOLUTION!!! There is no value for x that would make it true.

9.  3(3x + 5) = 9x + 15 I need to use the Distributive property first. -9x - 9x 15 = 15 9x + 15 = 9x + 15 This is true…but what happened to my x ??? If you get a situation like this – the answer is INFINITE SOLUTIONS!!! Any value that you substitute for x will make it a true statement. Okay ????