You can find the smallest possible answer to 3a - 2b, by using the lowest value for a and the highest value for b. This would be 3(6) - 2(5) which is the same as (3 x 6) - (2 x 5). This is equal to 18 - 10. The answer for the smallest possible value of 3a - 2b is 8.
To find the highest possible value, use the highest value for a and the lowest value for b. This would be 3(7) - 2(4) which is the same as (3 x 7) - (2 x 4). This is equal to 21 - 8. The answer for the smallest possible value of 3a - 2b is 13.
To check your answers, think about all the possible combinations you could have for a and b.
OPTION 1: A= 6, b=4: 3(6) - 2(4) (solution: (3x6)-(2x4) = 18 - 8 = 10)
OPTION 2: A= 6, b=5: 3(6) - 2(5) (solution: (3x6)-(2x5) = 18 - 10 = 8)
OPTION 3: A=7, b=4: 3(7) - 2(4) (solution: (3x7)-(2x4) = 21 - 8 = 13)
OPTION 4: A=7, b=5: 3(7) - 2(5) (solution: (3x7)-(2x5) = 21 - 10 = 11)
If you put these in order from highest to lowest, you can see which numbers to use for a and b to get the highest and lowest answers.
OPTION 3: 13 (a=7 and b=4)
OPTION 4: 11 (a=7 and b=4)
OPTION 1: 10 (a=6 and b=4)
OPTION 2: 8 (a=6 and b=5)
