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

+ = −

+ = +

− = +

+ + = − +

− = −

− + =

− + = − −