 # Solving Multi- Step Equations. And we don’t know “Y” either!!

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Solving Multi- Step Equations

And we don’t know “Y” either!!

Simplifying Algebraic Expressions Like Terms Example: -3x + 4y + 5x The Like terms are: -3x and 5x To simplify any expression, we need to combine all it’s like terms and perform as many operations as possible. 2x + 4y

Simplifying Algebraic Expressions Review Problems: 12 d - 6 + 4d 5 - 3m + 17 - 23m 4(7 - 3r) 16 d - 6 2 - 26m 2828 - 12r

Solving Multi-Step Equations Solve: 3n + 9 + 4n = 2 1. Combine like terms on same side of equal sign 7n + 9 = 2 2. Subtract 9 from each side 7n + 9 = 2 - 9 3. Simplify 7n7n =-7 4. Divide each side by “7” to get “n” by itself 7n = - 7 7 7 n = -1

Solving Multi-Step Equations Check: 3n + 9 + 4n = 2 1. Replace each “n” with “-1” 3(-1) + 9 + 4(-1) = 2 2. Simplify -3 + 9 + -4 = 2 6 22 =

Solving Multi-Step Equations Solve: 2m + 8 - 4m = 28 1. Combine like terms on same side of equal sign -2m + 8 = 28 2. Subtract 8 from each side -2m + 8 = 28 - 8 3. Simplify -2m-2m =2020 4. Divide each side by “-2” to get “m” by itself -2m = 20 -2 -2 m = - 10

Solving Multi-Step Equations Check: 2m + 8 - 4m = 28 1. Replace each “m” with “-10” 2(-10) + 8 - 4(-10) = 28 2. Simplify -20 + 8 + 40 = 28 -12 2828 28 =

Solving Multi-Step Equations Solve: 4(m + 3) = -32 1. Distributive Property 4(m + 3) = -32 4m4m + 12 = - 32 2. Subtract “12” from both sides 4m + 12 = -32 - 12 -12 3. Simplify 4m4m =-44 4. Divide each side by “4” to get “m” by itself 4m = -44 4 4 m = - 11

Solving Multi-Step Equations Solve: 3(x - 10) = 36 1. Distributive Property 3(x - 10) = 36 3x3x - 30 = 36 2. Add “30” from both sides 3x - 30 = 36 + 30 +30 3. Simplify 3x3x =66 4. Divide each side by “3” to get “x” by itself 3x = 66 3 3 x = 22

Solving Multi-Step Equations Solve: 7 + 3h = -1 - 5h 1. All variable terms need to be brought to one side 7 + 3h = -1 - 5h +5h + 5h 2. Subtract “7” from each side 7 + 8h = -1 -7 -7 8h = -8

Solving Multi-Step Equations 3. Divide each side by “8” to get “h” by itself h = -1 8h = -8 8

Solving Multi-Step Equations Solve: 2 + 14z = -8 + 9z 1. All variable terms need to be brought to one side 2 + 14z = -8 + 9z - 9z 2. Subtract “2” from each side 2 + 5z = -8 -2 -2 5z = -10

Solving Multi-Step Equations 3. Divide each side by “5” to get “z” by itself z = -2 5z = - 10 5 5

Solving Multi-Step Equations Solve: 5(x - 12) = -x 1. Distributive Property 5(x - 12) = -x 5x5x - 60 = -x 2. Bring all variable to one side 5x - 60 = -x - 5x -5x 3. Simplify -60 =-6x

Solving Multi-Step Equations 4. Divide each side by “-6” to get “x” by itself x = 10 -60 = - 6x -6 -6

Solving Multi-Step Equations Solve: 8(4 - a) = 2a 1. Distributive Property 8(4 - a) = 2a 3232 - 8a = 2a 2. Bring all variable to one side 32 - 8a = 2a +8a 3. Simplify 32=10 a

Solving Multi-Step Equations 4. Divide each side by “10” to get “a” by itself a = 3.2 32 = 10a 10 10

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