The document discusses solving equations by using inverse operations such as addition and subtraction to isolate the variable. It provides examples of solving one-step and multi-step equations, as well as using proportions to solve word problems involving rates, conversions, and recipes. Key terms discussed include coefficients, constants, variables, and inverse operations.

1. Equations Live Chat #3 Instructor: Tonya Andry-Stelter

2. What Does it Mean to Solve an Equation? To solve an equation means to find every number that makes the equation true. We do this by adding or subtracting to each side of the equation … but always keep it balanced!

3. What are the parts of an equation? Let’s first take a look at an equation and identify its parts Coefficient Constant Variable

4. So do we just use trial and error to find the right value? No. We can use inverse operations to isolate, or solve for, the variable’s value. Inverse operations? Think about it … The inverse operation of addition is subtraction . And the inverse operation of multiplication is division .

5. Solving 1 Step Equations How much does the suitcase weigh in terms of blocks? B=Blocks S=Suitcase Equation: 6B + S = 9B -6B -6B 3B S = What is the weight of the suitcase if each block has a weight of 2lbs. ? S = 3 (2) = 6 lbs.

6. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: - 13 Answer: - 13 Now that we have solved the equation, let’s check the solution:

7. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: + 5 Answer: + 5 Now that we have solved the equation, let’s check the solution:

8. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: Step 2: 25 Answer: 25 Now that we have solved the equation, let’s check the solution:

9. So how do we solve equations with inverse operations? Let’s take a look at a simple equation Step 1: Step 2: (16) Answer: (16) Now that we have solved the equation, let’s check the solution:

10. 1 Step Equation X + 11 = 9 X - 37 = 52 3X = 72 -11 -11 X = -2 3 3 X = 24 1 1 20 + h = 41 17 - s = 27

11. 1 Step Equations Continued… X / 5 = 10 X / 7 = 4 6X = 42 P = 3 / s = 21 2 5 3 4

12. Multi Step Equations Solve: 8m – 10 = 36 8m – 10 = 36 8m = 46 8 8 m = + 10 + 10

13. Multi Step Equations 5x  2 = x + 4 Solve: 5x  2 = x + 4 Notice that there are variables on both sides 5x = x + 6 Get rid of the -2 on the left side Simplify 5x = x + 6 Get rid of the x on the right side 4x = 6 Get rid of the coefficient of x 4 4 x = Simplify Simplify + 2 + 2 – x – x

14. Solving a Proportion Solve the proportion below 12 12

15. Solving a Proportion Solve the proportion below 52 52

16. Checking the Solution to a Proportion Let’s check the solution to the proportion we solved on the last slide 2

17. Using Proportions to Solve Problems You get 46 miles to a gallon of gas. How far can you go on 16 gallons of gas?

18. Word Problems A company purchased 5,000 pairs of men’s slacks for $15.86 per pair and marked them up $24.54. What was the selling price for each pair of slacks? Use the formula S=C+M. S=selling price, C=Original Cost, M=Mark up.

19. Fishing Pole Price Tracee and her husband bought a fishing pole for $62.45 for their weekend camping trip. The store they bought the poles from had marked them up $27.35. What was the original cost of the fishing poles for the store? Use the formula S = C + M

20. Two part time employees share one full-time position. Rosalind works Mondays, Wednesdays, Fridays and Saturdays. Sherman works Tuesdays and Thursdays. The job pays an annual salary of $45, 679. What annual salary does each employee earn? Annual Earnings

21. Money Conversion Tyesha is moving to Germany in the summer. She will need to convert some of her money before she leaves. If 1.00 US Dollar is equal to 0.734916 Euros then how much money should she expect to get if she converts $650?

22. Material Cost Veronica is an inspector who also buys material for the job site. She needs to buy 3 times as many yards of soil as yards of concrete. If a yard of concrete costs about $70 and a yard of soil costs about $57 and her total order was roughly $8378 how many yards of each did she order? $8378 = $70C + $57S Total Cost = Concrete Cost + Soil Cost 3 times as much soil as concrete S = 3C $8378 = $70C + $57(3C) $8378 = $70C + $171C $8378 = $241C $8378 $241 = C C ≈ 34.76 yds S = 3(34.76) S = 104.28yds.

23. Using Proportions to Solve Problems Your trimmer uses fuel that is a 1:50 ratio of oil to gas. If you have 68oz of gas, how much oil should you add?

24. Recipes (Proportions) Dawn enjoys cooking and wants to make a tasty dessert for her family. Her recipe uses 3 cups of sugar to 2 ¼ cups of flour. But she only has 2 cups of sugar, how much flour should you use? = Recipe Sugar Recipe Flour = New Amount of Sugar New Amount of Flour 3 ● X = = 2 ● 9/4 3X = 4.5 X = 1.5 3 2 ¼ 2 X