Solving Linear Equations

Multi-Step

100

-18k-6k=6+18k

k=-1

200

-7x+41+6x=36

x=5

300

-4k+10k-12=-3k-39

k=-3

400

-2x+y=9-4x

Solve for x

2x+y=9

2x=9-y

x=(9=y)/2

500

4x-2=3x-2

x=0

Distributive

100

3m=5(m+3)-3

m=-6

200

-12x-9+4(6x+1)=43

x=4

300

2(3x-4)=3x+1

x=3

400

65-4x=4-3(3x-2)

x=-11

500

3x=2x-(x+12)

x=-6

Rational

100

1/3x+2/3=17/3-5/3x

x=5/2

200

-6=3/5x

x=-10

300

3/4x=1/2 

x=2/3 

400

1/2+2/5x-1=1/5x+x

x=-5/8

500

1/4x+x=-3+1/2x 

x=-4

Distributive & Rational

100

2/3(3x-12)=3/4(8x+4)

x=-11/4 

200

1/5(2x-10)+4x=-3(1/5x+4)

x=-2

300

3/4(2x+1)+5/4=2

x=0

400

2/3(3x+1)=5

x=13/6

500

2/5(x-2)=-3x

x=4/17

Number of Solutions

100

7x+3=7x-3

No solution 

200

12x-1=-1+12x

Infinite Solutions

300

For what values of a and b would the equation have infinite solutions?

8x+2=ax+b

a=8

b=2

400

For what values of a and b would the equation have no solution?

8x+2=ax+b

a=8

b= anything but 2

500

For what values of a and b would the equation have one solution?

8x+2=ax+b

a= anything but 8

b=anything