1. 1. Simplify each side SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES 2. Get rid of variable on right side 3. Solve two step equation Get rid of parentheses, add like terms, etc. Add or subtract or use symmetric property. Add or subtract; then multiply or divide.

2. EXAMPLE 5x – 3 = 3x + 7 -3x 2x – 3 = 7 GET RID OF THE VARIABLE ON THE RIGHT SIDE SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES +3 2x = 10 2 x = 5 SOLVE 2-STEP EQUATION check: 5(5) – 3 = 3(5) + 7 25 – 3 = 15 + 7 22 = 22 ☺

3. EXAMPLE 7 = 7(x – 3) 7x – 21 = 7 GET RID OF THE VARIABLE ON THE RIGHT SIDE SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES +21 7x = 28 7 x = 4 SOLVE 2-STEP EQUATION SIMPLIFY BOTH SIDES 7 = 7x – 21 SYMMETRIC PROPERTY check: 7 = 7(4 – 3) 7 = 7(1) 7 = 7 ☺

4. EXAMPLE 2(m – 3) + 5 = 3(m – 1) -m – 1 = -3 GET RID OF THE VARIABLE ON THE RIGHT SIDE SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES +1 -m = -2 m = 2 SOLVE 2-STEP EQUATION SIMPLIFY BOTH SIDES 2m – 1 = 3m - 3 -3m check 2(2 – 3) + 5 = 3(2 – 1) -2 + 5 = 3 ☺

5. 2.3RATIOS & PROPORTIONS A RATIO is a comparison of two numbers by division. ♣ ♠ ♠ ♠ ♠ ♠ ♣ ♣ Using the diagram at right, what is the ratio of spades to clubs? 5:3 or 5 / 3 or 5 to 3

6. RATIOS & PROPORTIONS A RATIO is a comparison of two numbers by division. In a recipe, if you are to use 2 cups of flour and 1 teaspoon of baking soda. What is the ratio of flour to baking soda? 2 cups:1 tsp Units must be included

7. RATIOS & PROPORTIONS A RATIO is a comparison of two numbers by division. If Warren can read 120 pages in two days, what is the ratio of pages read to days. 60 pages:1 day The ratio of two measurements having different measures is called a RATE.

8. RATIOS & PROPORTIONS Other examples of rates. 200 miles in 4 hours 50 miles/hour $5.20 for 24 eggs $2.60 / dozen $48 for 15 gallons of gas $3.20 / gallon

9. RATIOS & PROPORTIONS A PROPORTION is an equation stating that two ratios are equal. extremes means In a proportion, the product of the means is equal to the product of the extremes.

10. RATIOS & PROPORTIONS How do we know it is a proportion? Cross Multiply (Means = Extremes) 20 Yes, it is a proportion!

11. RATIOS & PROPORTIONS How do we know it is a proportion? Cross Multiply (Means = Extremes) 39 40 No, it is not a proportion!

12. RATIOS & PROPORTIONS Solving a proportion Cross Multiply (Means = Extremes) 2x 21 2x = 21 x = 21 / 2

13. RATIOS & PROPORTIONS Solving a proportion Cross Multiply (Means = Extremes) 2x - 4 15 2x - 4 = 15 2x = 19 x = 19 / 2

14. PROBLEM SOLVING USING PROPORTIONS If Jenny can travel 520 miles in 9 hours, how far can she travel in 15 hours? 9x 7800 9x = 7800 x = 866.7 miles 866.7 miles x = distance traveled in 15 hours

15. PROBLEM SOLVING USING PROPORTIONS If Al can read 1240 words in 3 minutes, how many words can he read in 20 minutes? 3x 24800 3x = 24800 x = 8266.7 words 8266.7 words x = words read in 20 minutes

16. PRACTICE – Variables on both sides Solve: 3(x + 2) = 4(x – 5) + 2 3x + 6 = 4x – 20 + 2 3x + 6 = 4x – 18 -4x -x + 6 = -18 -6 -x = -24 x = 24

17. PRACTICE – Ratios & Proportions Solve: 4x + 20 = 3x - 6 -3x x + 20 = -6 -20 x = -26 Cross Multiply

18. PRACTICE – page 58 #3 Solve:

19. PRACTICE – page 58 #8 Solve:

20. PRACTICE – page 58 #9 Solve:

21. PRACTICE – page 58 #10 Solve:

22. PRACTICE – page 58 #11 Solve:

23. PRACTICE – page 58 #12 Solve:

24. PRACTICE – Ratios & Proportions Solve: 4x + 20 = 3x - 6 -3x x + 20 = -6 -20 x = -26 Cross Multiply

25. PRACTICE – Ratios & Proportions Solve: 4x + 20 = 3x - 6 -3x x + 20 = -6 -20 x = -26 Cross Multiply

26. PRACTICE – page 58 #8 Solve: