1. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Extension of AF4.1 Solve two-step linear equations in one variable over the rational numbers. California Standards

2. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations A multi-step equation requires more than two steps to solve. To solve a multi-step equation, you may have to simplify the equation first by combining like terms.

3. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Solve. 8x + 6 + 3x – 2 = 37 Additional Example 1: Solving Equations That Contain Like Terms 11x + 4 = 37 Combine like terms. – 4 – 4 Since 4 is added to 11x, subtract 4 from both sides. 11x = 33 x = 3 Since x is multiplied by 11, divide both sides by 11. 33 11 11x 11 = 8x + 3x + 6 – 2 = 37 Commutative Property of Addition Notes

4. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Solve. 9x + 5 + 4x – 2 = 42 Check It Out! Example 1 13x + 3 = 42 Combine like terms. – 3 – 3 Since 3 is added to 13x, subtract 3 from both sides. 13x = 39 x = 3 Since x is multiplied by 13, divide both sides by 13. 39 13 13x 13 = 9x + 4x + 5 – 2 = 42 Commutative Property of Addition Elbow Partners

5. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable. Notes – Give an example

6. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Solve. + = – Additional Example 2A: Solving Equations That Contain Fractions 3 4 7 4 5n5n 4 Multiply both sides by 4. ( ) ( ) ( ) 5n 4 7 4 –3 4 4 + 4 = 4 5n + 7 = –3 Distributive Property ( ) ( ) ( ) 5n 4 7 4 –3 4 4 + 4 = 4 Simplify. Notes

7. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Additional Example 2A Continued 5n + 7 = –3 – 7 –7 Since 7 is added to 5n, subtract 7 from both sides. 5n = –10 5n5n 5 –10 5 = Since n is multiplied by 5, divide both sides by 5 n = –2 Notes Continued

8. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations The least common denominator (LCD) is the smallest number that each of the denominators will divide into evenly. Remember! Give your face partner an example of this

9. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Solve. + = – Check It Out! Example 2A 1 4 5 4 3n3n 4 Multiply both sides by 4. 5 4 –1 4 3n3n 4 4 + = 4 ( ) ( ) ( ) ( ) ( ) 3n 4 5 4 –1 4 4 + 4 = 4 3n + 5 = –1 Distributive Property ( ) ( ) ( ) 3n 4 5 4 –1 4 4 + 4 = 4 Simplify. 1 1 1 1 1 1 Rally Coach A

10. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Check It Out! Example 2A Continued 3n + 5 = –1 – 5 –5 Since 5 is added to 3n, subtract 5 from both sides. 3n = –6 3n3n 3 –6 3 = Since n is multiplied by 3, divide both sides by 3. n = –2

11. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Solve. + – = Check It Out! Example 2B 1 3 x 3 5x5x 9 13 9 9 ( ) + 9 ( ) – 9 ( ) = 9 ( ) 5x5x 9 x 3 13 9 1 3 5x + 3x – 13 = 3 x 3 1 3 5x5x 9 13 9 ( ) ( ) 9 + – = 9 Distributive Property Multiply both sides by 9, the LCD. 9 ( ) + 9 ( ) – 9 ( ) = 9 ( ) 5x5x 9 x 3 13 9 1 3 Simplify. 1 1 1 3 1 1 1 3 Rally Coach B

12. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations 8x = 16 = 8x8x 8 16 8 Since x is multiplied by 8, divide t both sides by 8. x = 2 + 13 + 13 Since 13 is subtracted from 8x, add 13 to both sides. 8x – 13 = 3 Combine like terms. Check It Out! Example 2B Continued

13. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations On Monday, David rides his bicycle m miles in 2 hours. On Tuesday, he rides three times as far in 5 hours. If his average speed for the two days is 12 mi/h, how far did he ride on Monday? Round your answer to the nearest tenth of a mile. Additional Example 3: Travel Application David’s average speed is his total distance for the two days divided by the total time. average speed = Total distance Total time Put formula in notes

14. Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Additional Example 3 Continued Multiply both sides by 7. Substitute m + 3m for total distance and 2 + 5 for total time. 2 + 5 = 12 m + 3m 7 = 12 4m Simplify. 7 = 7(12) 7 4m 4m = 84 David rode 21.0 miles. Divide both sides by 4. m = 21 84 4 4m44m4 =