1. Solve Equations With Variables on Both Sides

2. Example 1 3x + 4 = 5x – 8 Since the x’s are on opposite sides of the equal sign, you must “get rid” of one of them by using inverse operations. I like to “get rid” of the one on the right side so that the x ends up on the left side. So, I will subtract 5x from both sides.

3. Example 1 3x + 4 = 5x – 8 3x – 5x + 4 = 5x – 5x – 8 Simplify -2x + 4 = -8 Now you can solve this equation! Subtract 4 from both sides. -2x + 4 – 4 = -8 – 4 -2x = -12 Divide both sides by –2 X = 6

4. Example 2 4(1 – 2x) = 4 – 6x 4 – 8x = 4 – 6x 4 – 8x + 6x = 4 – 6x + 6x -2x + 4 = 4 -2x + 4 – 4 = 4 – 4 -2x = 0 X = 0

5. Example 3 9 + 5x = 5x + 9 9 + 5x – 5x = 5x + 9 – 5x 9 = 9 Since all of the variables are gone, this is different. Does 9 = 9? Yes, so it is what we call an Identity (that means there are infinitely many answers). So, the answer is all real numbers (R).

6. Example 4 6x – 1 = 6x – 8 Subtract 6x from both sides. 6x – 6x – 1 = 6x – 6x – 8 -1 = -8 Again, both variables are gone. Is –1 = -8 true? No, so it is no solution (There aren’t any numbers that will work.) The answer is no solution or

7. From tonight’s work… #33 Justin and Tyson are beginning an exercise program to train for football season. Justin weighs 150 lb and hopes to gain 2 lb per week. Tyson weighs 195 lb and hopes to lose 1 lb per week. If the plan works, in how many weeks will the boys weigh the same?

8. Another one… Rapid Rental Car company charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $45 for rental and gas and $0.35 per mile. A. Find the number of miles for which the companies’ charges will be the same. B. The Barre family estimates that they will drive about 95 miles during their vacation. Which company should they choose? C.If they extend their vacation and travel about 120 miles. Should they rent from the same company?

9. Try these… 2x + 16 = x – 25 14 – (2x + 5) = -2x + 9 0.7m = 0.9m + 2.4 – 0.2m x + 1 = 4x + 1 5(x+7) = 2(x - 20) + x

10. Try these…-answers 2x + 16 = x – 25x = -41 14 – (2x + 5) = -2x + 9R 0.7m = 0.9m + 2.4 – 0.2m x + 1 = 4x + 1x = 0 5(x+7) = 2(x - 20) + x x = -37.5