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 d 5 - 3m m 4(7 - 3r) 16 d m r

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

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

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

Solving Multi-Step Equations Check: 2m m = Replace each “m” with “-10” 2(-10) (-10) = Simplify = =

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

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

Solving Multi-Step Equations Solve: 7 + 3h = h 1. All variable terms need to be brought to one side 7 + 3h = h +5h + 5h 2. Subtract “7” from each side 7 + 8h = h = -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: z = z 1. All variable terms need to be brought to one side z = z - 9z 2. Subtract “2” from each side 2 + 5z = z = -10

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

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 = = - 6x -6 -6

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

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