1. OBJECTIVE I will use the order of operations and rounding to find the exact and approximate solutions of equations that contain decimals.

2. Rounding for a Practical Answer Six people buy some food to take to the lake. The total cost for the food is $33.45. If each person pays the same amount, how much does each person owe? 6x = 33.45Original equation x = 5.575Exact answer x ≈ 5.58Round to the nearest cent Each person owes $5.58. The exact answer is not practical because you cannot have a fraction of a cent, but six times the rounded answer does not correspond to the cost of the food. It is one cent too much due to round-off error.

3. Rounding for the Final Answer Solve 7x + 32 = 128. Round to the nearest hundredth. 7x + 32 = 128Original equation 7x = 96Subtract 32 from each side x = 13.714…Divide both sides by 7 x ≈ 13.71Round to nearest hundredth The solution is approximately 13.71.

4. Guided Practice 1. Solve -12x - 13 = 37. Round to the nearest hundredth.

5. Original Equation Involving Decimals Solve using same methods used to solve equations without a decimal. Solve 2.14x + 3.81 = 0.53x + 14.96. Round to the nearest hundredth. 2.14x + 3.81 = 0.53x + 14.96 1.61x = 11.15 x = 6.925… x ≈ 6.93

6. Guided Practice 1. Solve 7.82x - 3.14 = 4.66x + 2.71. Round your answer to the nearest hundredth.

7. Changing Decimal Coefficients to Integers Change decimals to integers for easier calculation Solve 2.3x + 6.2 = 1.5x + 9.8. Round to the nearest tenth. 2.3x + 6.2 = 1.5x + 9.7 Original Equation 23x + 62 = 15x + 97Multiply both sides by 10 8x = 35Combine like terms x = 4.625 x ≈ 4.6

8. Guided Practice Re-write the coefficients as integers and solve. Round to the nearest tenth. 1. 5.7 - 3.4x = 2.2x - 7.1

9. Using a Verbal Model You are shopping for roses. The total tax is 10%. You have a total of $27.79 to spend. What is your price limit for the roses? Total cost is price limit and tax based on price limit.

10. Using a Verbal Model Cost of Roses + Cost of Tax = Price Limit x + 0.10x = 27.79Substitute 1.10x = 27.79Combine like terms x = 25.263…Divide both sides by 1.10 x ≈ 25.26Round down You have a limited amount of money to spend, so you must round down to $25.26. If you round up, the tax and total cost will increase and you will be a penny short.

11. Guided Practice You are shopping for a bracelet. The sales tax is 5%. You have a total of $125.40 to spend. What is your price limit for the bracelet?

12. Independent Practice Round answers to the nearest hundredth. 1.3x + 5 = 20 2.2.51x - 4.27 = 1.13x + 2.15 3.Change the decimal coefficients to integers to solve. 3.4x - 2.3 = 1.7x + 5.4