Category 1: SOLVE
Category 2: SOLVE
Category 3: SOLVE
100

3x = 4x + 9

-9

100

9x= 18x

x = 0, x = 2

100

9x2 = 18

x = 12, x = -12

200

2(x-5) = -12

-1

200

x+ 50 = 27x 

x = 25, x = 2


200

7(x + 5)2 = 21

x = 5 plus root three, or 5 minus root three 


300

7x - 3(x - 2) = x - 3(x - 5) 

3/2

300

2x(x - 5) = -12 

x = 3, x = 2

300

3x2 + 5 = 65

x = +/- 2 root 5

400

4x - 3(2 - x) = 1/2 (14x-12) 

All real numbers


400

x2 + 7x - 4 = -x2

x = 1/2, x = -4

400

x3 + 2 = -25

x = -3

500

5(x - 7) = 2(4 - x) + x 

43/6

500

6x3 + 48x = 36x2

x = 0, x = 4, x = 2

500

3(x + 5)2 +1 = 37

-5 plus 2 root three 

-5 minus 2 root three