Unit 2 : One Variable Equations and Inequalities



Unit 2: One Variable Equations and Inequalities

Class Notes Day 2 – Solving Multistep Equations and Equations with the Variable on Both Sides

I. The Distributive Property

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4) [pic] 5) [pic]

II. Multistep Equations

Examples:

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9) [pic] 10) [pic] 11) [pic]

Practice:

12) 6n – 2n = -64 13) –15x + 10x – 7 = 108 14) 3y + 4y – y = 12

15) 2y + 4(y + 5 ) = -16 16) 40 = 5( 3x + 2 ) 17) 6x – 9x + 2x – 4 = 9 – 11

18) 6x – 4( 2x + 8 ) = 16 19) 2( 3 + 4n ) – 9 = 45 20) –5a + 4( 2 + 2a ) = -1

21) –8y + y + 12 = -23 22) –2( 2x + 3 ) – 4 = -8 + 15 – 5 23) 6y – 9y + 2y – 4 = -8

24) –3( 4 + 3x ) = -9 25) 3( 5 + 3x ) – 8 = 88 26) 2( 3x – 4 ) – ( x + 2 ) = -45

III. Equations with the Variable on Both Sides

Examples:

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4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic]

Practice:

9) 4x = 7x – 12 10) 9n – 22 = 4n + 3 11) 18n + n = 11 – 3n

12) 35n + 12 = 40n + 42 13) 3( x + 8 ) = 7x 14) 6( 7 – y ) + y = 36 + y

15) –4( 3x + 2 ) = 3( 6x – 6 ) 16) –5( x + 2 ) = 3( x + 2 ) 17) 8 + 3( a – 3 ) = 4( a + 5 )

IV. Homework

1) 8y – 2y + 4 = 22 2) 3( x – 4 ) = 15 3) 4( 5 – x ) = -9 + 5

4) –3( a – 7 ) + 3 = 0 5) –4k – 7 + 12k = -12 + 37 6) 19 = 3( 5x – 2 )

7) 2( 2x – 4 ) + 3x = 20 8) 9x – 5 + 6x = 27 + 13 9) 4r – ( r + 6 ) = 12 – 36

10) 3( x – 8 ) + 3( 2x + 4 ) = 15 11) 6y – 9y + 2y – 4 = -8 12) 3( 5 + 3x ) – 8 = 88

13) 15p + p = 7 – 12p 14) 8a – a = a + 24 15) 7y = y – 12

16) 11k - 23 = 12k + 5 17) 14b – 2 = 19b + 33 18) 4( 8 – 5u ) = -2u – 4

19) 7( a – 8 ) = 3( a + 4 ) 20) –7( 4x + 2 ) = 5( 2x + 1 ) 21) 16b – 4 = 38b + 84

22) 7( 7 – 3u ) = -u – 11 23) 8 + 3( a – 3 ) = 4( a + 5 ) 24) 6 – 2x + 5x = 7 + 7x - 15

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