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1) 8m - 1 =31
2) -6g +8 = -46
3)
4) 3p - p + 1 = -9
5) 5a - 10 = 0
6) 5q + 3q - 1 = -33
542x =−
01 September 2015 Warm-‐Up
Solve each equation and check the solution.
Multi-Step Equations
Multi-Step equations are just 2-Step equations on STEROIDS!
Remember these few simple rules!
1) Get rid of fractions by multiplying ALL terms by the largest denominator in the equation and then simplify. (Repeat as needed until all fractions are gone. Any fraction you need in the answer will appear at the end of the problem.)
2) Combine like terms. (Typically numbers on the right and variable terms on the left but it works the other way as well.)
3) Solve the problem like a simple 1-step equation.
Solving Simple Mul.-‐Step Equa.ons
8 4 7 11x x+ − =
= ?x
11x
Step 1: Combine Like Terms (There are no frac?ons with which to deal)
8 4 7x + −( )4 7 3− = −
8 3x −= ?x
11x8 3x −
Solving Simple Mul.-‐Step Equa.ons
8 4 7 11x x+ − =
= ?x
11x8 3x −
= ?x
03 3x− −
( )8 11 3x x x− = − ( )11 11 0x x− =
3 3x− − 0
3 3 0− + = 0 3 3+ =3x− 3
Solving Simple Mul.-‐Step Equa.ons
8 4 7 11x x+ − =
= ?x33x−
33x x−⎛ ⎞=⎜ ⎟−⎝ ⎠
3 13
⎛ ⎞= −⎜ ⎟−⎝ ⎠
1x = −
( ) ( )8 1 4 7 11 1 8 4 7 11 11 11
− + − = −
− + − = −
− = −
Solve like a 1-step equation
Check your answer!
Solving Simple Mul.-‐Step Equa.ons 3 1 164 2 3x x+ − =
= ?x13x
Step 1: Start by elimina?ng frac?ons Mul?ply everything by 4 (the biggest denominator).
Don’t forget to simplify.
3 164 2x + −
3 14 64 2x⎛ ⎞+ −⎜ ⎟
⎝ ⎠
143x⎛ ⎞
⎜ ⎟⎝ ⎠
( )( )
4 3 14 6 44 2x
⎛ ⎞⎛ ⎞+ −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
( )4 13x
⎛ ⎞⎜ ⎟⎝ ⎠12 424
4 2x + −
3 24 2x + −
43x
3 22x +43x
Solving Simple Mul.-‐Step Equa.ons 3 1 164 2 3x x+ − =
= ?x
Repeat Step 1 this ?me mul?plying everything by 3 to eliminate the last frac?on. Don’t forget to
simplify.
3 22x + 43x
( )3 3 22x + 433x⎛ ⎞
⎜ ⎟⎝ ⎠
( ) ( )3 3 3 22x + ( )3 43x
9 66x + 123x
4x9 66x +
Solving Simple Mul.-‐Step Equa.ons 3 1 164 2 3x x+ − =
= ?xStep 2: Solve the equa?on like a simple two-‐step
equa?on.
4x9 66x +
( )9 4 5x x x− = ( )4 4 0x x− =
5 66x + 0( )66 66 0− = ( )0 66 66− = −
5x 66−55x x= 66
5−
66 1135 5
x −= = −
Solving Simple Mul.-‐Step Equa.ons 3 1 164 2 3x x+ − =
Don’t FORGET to check you answer! 66 1135 5
x −= = −
3 66 1 1 6664 5 2 3 5
− −⎛ ⎞ ⎛ ⎞+ − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠198 1 66620 2 15− −⎛ ⎞ ⎛ ⎞+ − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
22 225 5− −
=
Solving Simple Mul.-‐Step Equa.ons
Solve each equation and check the solution.
( )( ) ( )
( )( )
1) 6 3 2 132) 3 1 7 53) 8 2 1 3 1
4) 5 2 4 5 3 10
5) 5 4 7 1 2
6) 7 2 1 2 9
K KN n
T T
k k
n n n
x x
− = +
+ = −
− + = − +
+ + = − +
+ = + −
+ + = +
Solving Simple Mul.-‐Step Equa.ons
Special Notes:
A) If you did problem #5 above correctly you ended up with 4 = 7 Since 4 does NOT equal 7 the only conclusion you can draw is that the equation has NO SOLUTION
B) If you did problem #6 above correctly you
ended up with 2N + 9 = 2N + 9 or 9 = 9
In both case you can use any number for N to make the equation true, therefore the only conclusion you can draw is that the equations has
INFINTELY MANY SOLUTIONS
September 01, 2015 Homework – Part 1
Copy and solve the following equa.ons. Check your answers.
( ) ( )
( )( )
( )
1) 3 5 3 12) 6 5 303) 5 2 3 24) 2 7 3
5) 3 1 5 3 2
6) 75 9 5 4 27) 1.2 4.3 2.18) 4.4 6.2 8.8 1.8
X XB B
Y Y YT T
A A
G GX XS S
− + = −
− = +
− = +
+ = −
+ − = −
− = − +
+ = −
+ = −
September 01, 2015 Homework – Part 2
Copy and solve the following equa.ons. Check your answers.
( ) ( )
( )
( ) ( )
( )( ) ( )
9) 5 2 2 31 110) 4 882 82 111) 3 25 5
12) 5 3 9 3 2 63 113) 5 14 4
14) 0.03 2 30 1.8
15) 5 2 3 3 11 4 58
F F
B B
W W W
P P
K K
G G
R R
+ = −
+ = +
− = +
+ + = − +
− = −
− + =
− + = − −