1. PRE-ALGEBRA

2. Lesson 7-3 Warm-Up

3. PRE-ALGEBRA How do you solve equations that involve fractions? How do you clear fractions from both sides of an equation? To solve equations involving fractions: 1. clear the equation of fractions first or undo fractions as you normally would using properties of equality. To clear fractions from both sides of an equation, multiply all of the terms by a common denominator (preferably the Lowest Common Denominator, or LCD) Example: Solve + = 17 3x 2 x5x5 Method 1: Use reciprocals (Division Property of Equality). + = 17 3x 2 x5x5 x + x=17 Rewrite as or x. 3232 1515 x + x=17 A common denominator of and is 10. 15 10 2 10 3232 1515 x=17 Combine like terms. 17 10 ( x )= (17) Multiply each side by the reciprocal of, which is. 17 10 10 17 17 10 10 17 x=10 x5x5 1x 5 1515 Two-Step Equations with Fractions and Decimals (7-3)

4. PRE-ALGEBRA 15x + 2x=170Multiply. 17x=170Combine like terms. x=10Simplify. Method 2: Multiply by the LCD to clear fractions. + = 17 3x23x2 x5x5 10 ( + ) =10(17)Multiply each side by 10, a common multiple of 2 and 5. 3x23x2 x5x5 10 ( ) + 10 ( ) =10(17)Use the Distributive Property. 3x23x2 x5x5 =Divide each side by 17. 17x 17 170 17 Two-Step Equations with Fractions and Decimals (7-3)

5. PRE-ALGEBRA Solve p – 7 = 11. p – 7 = 11 3434 Add 7 to each side.p – 7 + 7 = 11 + 7 3434 Simplify. p = 18 3434 p = 3434 4343 4343 18Multiply each side by, the reciprocal of. 3434 4343 1p = 4 18 3 1 6 Divide common factors. p = 24Simplify. 3434 Two-Step Equations With Fractions and Decimals LESSON 7-3 Additional Examples

6. PRE-ALGEBRA (continued) Simplify. 18 – 7 11 11 = 11 Check: p – 7 = 11 3434 (24) – 7 11Replace p with 24. 3434 – 7 11 Divide common factors. 3 24 4 Two-Step Equations With Fractions and Decimals LESSON 7-3 Additional Examples 1 6

7. PRE-ALGEBRA Solve y + 3 =. y + 3 = 1212 2323 Multiply each side by 6, the LCM of 2 and 3. 6y + 3 = 1212 6 2323 3y + 18 – 18 = 4 – 18Subtract 18 from each side. 3y = –14Simplify. 3y + 18 = 4Simplify. Use the Distributive Property. 6 y + 6 3 = 1212 6 2323 Divide each side by 3. 3y33y3 –14 3 = Simplify.y = –4–4 2323 2323 1212 Two-Step Equations With Fractions and Decimals LESSON 7-3 Additional Examples

8. PRE-ALGEBRA Example: Solve 0.6a + 18.65 = 22.85. 100(0.6a + 18.65) = 100(22.85) The greatest number of decimal places is two places, so multiply each side by 10 2 or 100. 100(0.6a) + 100(18.65) = 100(22.85) Use the Distributive Property. 60a + 1865= 2285 Simplify. 60a + 1865 = 2285 - 1865 - 1865 Subtract 1865 from each side. 60a = 420 Simplify. a=7 Simplify. = Divide each side by 60. 60a 60 420 60 How do you clear solve equations that involve decimal? How do you clear decimals? To solve equations involving decimals, it might be easier to clear the equation decimals first. To clear decimals from both sides of an equation, multiply all of the terms by by the power of 10 that would move the decimal with the greatest number of decimal places to the end to make a whole number. Two-Step Equations with Fractions and Decimals (7-3)

9. PRE-ALGEBRA Suppose your cell phone plan is $30 per month plus $.05 per minute. Your bill is $36.75. Use the equation 30 + 0.05x = 36.75 to find the number of minutes on your bill. There are 135 minutes on your bill. 30 + 0.05x = 36.75 x = 135Simplify. 3000 – 3000 + 5x = 3675 – 3000Simplify and subtract 3000 from each side. 5x = 675Simplify. Divide each side by 0.05.= 675 5 5x55x5 Two-Step Equations With Fractions and Decimals LESSON 7-3 Additional Examples 100(30) + 100(0.05x) = 100(36.75) The greatest number of decimal places is two places, so multiply each side by 10 2 or 100.

10. PRE-ALGEBRA Solve each equation. 1. d + 13 = 20 2. (s – 8) = 93.5 + = 14 4.0.07x + 0.03 = 0.385.0.015w – 1.85 = 1.615 1616 3535 2c42c4 422318 5231 Two-Step Equations With Fractions and Decimals LESSON 7-3 Lesson Quiz