Algebra Core 2 Math Jeopardy-Elizabeth and Angelina

Distributive property

100

2(4x-3)=2

8x-6=2 

8x=8

x=1

200

5x+3(7x+2)=2x+3 

5x+3(7x+2)=2x+3 

5x+21x+6=2x+3 

26x+6+2x+3 

24x=-3 

x=-8

300

4y+4+4(4y+4)=4+4+5y

4y+4+4(4y+4)=4+4+5y 

4y+4+16y+16=8+5y 

20y+20=8+5y 

15y=-12 

y=-12/15

400

3z+4z+6(7z+12z)+4z+5=2z

3z+4z+6(7z+12z)+4z+5 

3z+4z+42z+72z+4z+5=2z

125z+5=2z

5=-123z 

z=-24.6

500

6x+7x+8(3x+1/2)=7x+3+2

6x+7x+8(3x+1/2)=7x+3+2

6x+7x+24x+4=7x+3+2 

37x+4+7x+5 

30x=1 

x=1/30

Identity/no solution

100

k-3k=6k+-8k

k-3k=6k+-8k

k-2k=-2k+5

0k=5 

No solution 

200

2(a-4)=4a-(2a+4) 

2(a-4)=4a-(2a+4) 

2a-8=4a-2a-4 

2a-8=2a-4 

-8=-4

No solution

300

-6a+3=-3(2a-1)

-6a+3=-3(2a-1) 

-6a+3=-6a+3 

3=3

Identity

400

10+6x=15+9x-3x

10+6x=15+9x-3x 

10+6x=15+6x 

10=15 

no solution 

500

3x+5=3x-2

3x+5=3x-2 

3x-3x=-2-5

0=-7

no solution 

fractions

100

1/2(4x+20/2)=8x

1/2(-4x+20/2)=8x 

-2x+5=8x

5=10x 

x=2

200

3/4(x+3)=9 

3/4(x+3)=9 

4(3/4x+9/4)=(9)4 

3x+9=36 

3x=27 

x=9

300

2/5x-3=1/2

2/5x-3=1/2 

5/2(2/5x)=(7/2)5/2 

x=35/4

400

-1/3x=12

-1/3x=12 

x=-36

500

1/3x+2/7=2

1/3x+2/7=2 

1/3x=2-2/7 

14/7-2/7=12/7 

1/3x=12/7 

x=36/7 or 5 1/7 

literal equations

100

solve for x

x+a=n

x+a=n 

x=n-a

200

solve for x

dwx=q

dwx=q 

x= q/dw

300

solve for x

c(x+q)=5n

c(x+q)=5n 

x+q=5n/c 

x=5n/c-q

400

solve for x

6x+w=c

6x+w=c 

x= c-w/6

     

500

solve for y 

5(y-x)=y

5(y-x)=y 

5y-5x=y

-5x=-4y 

y=5x/5

Misc.

100

2(x-6) =-5x-12+7x

2(x-6) =-5x-12+7x

2x-12=2x-12 

-12=-12 

identity

200

I always make a carrot pie for Christmas dinner. I can peel 4 carrots per minute. For the recipe, I need 80 carrots. How long will it take me to finish if I've already peeled 20 carrots? 

4x+20=80 

4p=60 

p=15 

15 minutes

300

simplify 

4a-2(3a+7)

4a-2(3a+7) 

4a-6a-14 

-2a-14

400

solve for z

dz-wz=-q

dz+wz=q 

z(d+w)=q 

z=q/d+w

500

3x+5-x=2x+7

3x+5-x=2x+7 

2x+5=2x+7 

0=2 

no solution