Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve. 1. 3x = 102 2. = 15 3. z – 100 = 21 4. 1.1 + 5w = 98.6 x = 34 y 15 y = 225 z = 121 w = 19.5

Learn to solve multi-step equations.

Additional Example 1A: Solving Equations That Contain Like Terms Solve. 8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms. – 4 – 4 Subtract 4 from both sides. 11x = 33 33 11 11x = Divide both sides by 11. x = 3

Additional Example 1A Continued Check 8x + 6 + 3x – 2 = 37 8(3) + 6 + 3(3) – 2 = 37 ? Substitute 3 for x. 24 + 6 + 9 – 2 = 37 ? 37 = 37 ? 

Additional Example 1B: Solving Equations That Contain Like Terms Solve. 4(x – 6) + 7 = 11 4(x – 6) + 7 = 11 Distributive Property 4(x) – 4(6) + 7 = 11 Simplify by multiplying: 4(x) = 4x and 4(6) = 24. 4x – 24 + 7 = 11 4x – 17 = 11 Simplify by adding: –24 + 7 = 17. + 17 +17 Add 17 to both sides. 4x = 28 Divide both sides by 4. 4 x = 7

Check It Out: Example 1 Solve. 9x + 5 + 4x – 2 = 42 13x + 3 = 42 Combine like terms. – 3 – 3 Subtract 3 from both sides. 13x = 39 39 13 13x = Divide both sides by 13. x = 3

Check It Out: Example 1 Continued 9x + 5 + 4x – 2 = 42 9(3) + 5 + 4(3) – 2 = 42 ? Substitute 3 for x. 27 + 5 + 12 – 2 = 42 ? 42 = 42 ? 

If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) of the fractions. This step results in an equation without fractions, which may be easier to solve.

The least common denominator (LCD) is the smallest number that each of the denominators will divide into. See Lesson 5.3 – Video Example 2 Remember!

Additional Example 2: Solving Equations That Contain Fractions Solve. + – = x 2 7x 9 17 2 3 The LCD is 18. ( ) ( ) x 2 3 7x 9 17 18 + – = 18 Multiply both sides by 18. 18( ) + 18( ) – 18( ) = 18( ) 7x 9 x 2 17 3 Distributive Property. 14x + 9x – 34 = 12 23x – 34 = 12 Combine like terms.

Additional Example 2 Continued 23x – 34 = 12 Combine like terms. + 34 + 34 Add 34 to both sides. 23x = 46 = 23x 23 46 Divide both sides by 23. x = 2

Additional Example 2 Continued Check x 2 7x 9 17 2 3 + – = 2 3 Substitute 2 for x. 7(2) 9 + – = (2) 17 ? 2 3 14 9 + – = 17 ? 2 3 14 9 + – = 17 ? 1 The LCD is 9. 6 9 14 + – = 17 ? 6 9 = ? 

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 14

Lesson Quiz Solve. 1. 6x + 3x – x + 9 = 33 2. 8(x + 2) + 5 = 29 x = 3 3. + = 5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate? x = 3 x = 1 5 8 x 8 33 8 x = 28 x = 1 9 16 25 21 4. – = 6x 7 2x 21 $8.50

Lesson Quiz for Student Response Systems 1. Solve 4p + 13 + 11p = 88 A. p = 5 B. p = 7 C. p = 75 D. p = 91 16

Lesson Quiz for Student Response Systems 2. Solve 4(x + 3) + 5 = 109 A. x = 4 B. x = 23 C. x = 26 D. x = 101 17

Lesson Quiz for Student Response Systems 3. Solve . A. x = 5 B. x = 6 C. x = 21 D. x = 101 18