1. ALGEBRA 1 Lesson 2-2 Warm-Up

2. ALGEBRA 1 Lesson 2-2 Warm-Up

3. ALGEBRA 1 “Solving Multi-Step Equations” (2-2) What are the steps for solving a multi-step equation? Step 1: Clear the equation of fractions and decimals. You can clear decimals by using the decimal that has the most digits after it and moving all of the decimals that number of jumps to the right. Example: 0.5a 2 + 0.875 = 13.25 Since 0.875 is the greatest number of place values from the end (3), jump all of the decimals 3 places to the right, so 0.5a 2 + 0.875 = 13.25 is the same as 500a 2 + 875 = 13,250 Step 2: Use the Distributive Property to remove parenthesis if you can’t simplify the problem within them. Step 3: Combine like terms on each side. Step 4: “Undo” (since you’re working backwards) addition and subtraction. Step 5: Undo multiplication and division.

4. ALGEBRA 1 Solve 3a + 6 + a = 90 4a + 6=90Combine like terms. 4a + 6=90 Subtract 6 from each side. -6 - 6 4a =84Simplify. 3a + 6 + a=90 Check: 90=90 63 + 6 + 2190 3(21) + 6 + 2190 Substitute 21 for a. a=21Simplify. =Divide each side by 4. 4a44a4 84 4 Solving Multi-Step Equations LESSON 2-2 Additional Examples

5. ALGEBRA 1 You need to build a rectangular pen in your back yard for your dog. One side of the pen will be against the house. Two sides of the pen have a width of x ft and the length will be 25 ft. What is the greatest width the pen can be if you have 63 ft of fencing? Words: width plus 25 ft plus width equals amount of side of side of fencing Define: Let x = width of a side Equation: x + 25 + x = 63 Solving Multi-Step Equations LESSON 2-2 Additional Examples

6. ALGEBRA 1 x + 25 + x=63 The pen can be 19 ft long. 2x + 25=63Combine like terms (1x + 1x = 2x). 2x + 25=63Subtract 25 from each side. - 25 - 25 2x = 38Simplify. x=19 (continued) =Divide each side by 2. 2x22x2 38 2 Solving Multi-Step Equations LESSON 2-2 Additional Examples

7. ALGEBRA 1 Solve 2(x – 3) = 8 2x – 6=8Use the Distributive Property. 2x – 6=8Add 6 to each side. + 6 + 6 2x = 14Simplify. x=7Simplify. =Divide each side by 2. 2x22x2 14 2 Solving Multi-Step Equations LESSON 2-2 Additional Examples

8. ALGEBRA 1 Solve + = 17 3x23x2 x5x5 x=10 Simplify. Method 1: Finding common denominators + = 17 3x23x2 x5x5 x + x=17 Rewrite the equation. 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 + x=17 A common denominator of and is 10. 15 10 2 10 3232 1515 Solving Multi-Step Equations LESSON 2-2 Additional Examples

9. ALGEBRA 1 15x + 2x=170Multiply. 17x=170Combine like terms. x=10Simplify. Method 2: Multiplying 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 (continued) Solving Multi-Step Equations LESSON 2-2 Additional Examples

10. ALGEBRA 1 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 Subtract 1865 from each side. - 1865 - 1865 60a =420 Simplify. a=7 Simplify. = Divide each side by 60. 60a 60 420 60 Solving Multi-Step Equations LESSON 2-2 Additional Examples

11. ALGEBRA 1 Solve each equation. 1. 4a + 3 – a = 242. –3(x – 5) = 66 3. + = 74. 0.05x + 24.65 = 27.5 n3n3 n4n4 7–17 1257 Solving Multi-Step Equations LESSON 2-2 Lesson Quiz