help with these questions...?

Question

ok these are for my homework but i need and explanation with it.
watts the variable?
when f-20/3 + 6 = 12.

how do you use the distributive property to FACTOR this?
16t-4, and 80z +45
P.S how do u factor any problems?

thanks

Answer 1

what do you mean the variable?

f - 20/3 + 6 = 12

f - 20/3 = 12 - 6

f - 20/3 = 6

f (3) - 20/3 = 6 [ f times 3 to make the denominator the same ]

3f - 20 = 6 x 3 [ the 3 is brought to the other side ]

3f -20 = 18

3f = 18 + 20

3f = 38

f = 38/3

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16t - 4
answer = 4 ( 4t - 1 )


80z + 45
answer = 5 (16 + 9 )

: you take out the number that can be divided by both numbers. The unknown is ignored. This is called factorisation.



Hope this helps.

Answer 2

f - 20/3 = 6
f = 6 + 20/3
= 38/3

16t - 4 = 4(4t - 1)
80z + 45 = 5(16z + 9)

To factorize a polynomial, you have to find the common factor in each of the terms. For eg. the common factor in both the terms of 16t - 4 was 4 so you have to take out 4 from each term and then write the rest in the bracket.

Answer 3

(f - 20) / 3 + 6 = 12
eliminate the denominator by multiplying 3 to either side:
f - 20 + (3)(6) = (3)(12)
f - 20 + 18 = 36
then just simplify, ending with f = 38.

notice that 16t and -4 are both divisible by 4.
remember the distributive property: a(b + c) = ab + ac.
16t - 4 can then be defined as (4)(4t) + (4)(-1)
(4)(4t) + (4)(-1) actually is a lot like ab + ac, with a = 4. according to the distributive property: ab + ac = a(b + c). you can then re-arrange the equation in that form, by factoring the 4 outside.
(4)(4t) + (4)(-1) = (4)(4t - 1)
do the same for the second problem, and just figure out their greatest common factor (GCF), the greatest number which both of them are divisible to. re-arrange the problem by using the distributive property.

Answer 4

make the fraction positive (ie change the side), subtract 6 from each side and finally make all the values into one value.

factorizing means taking out a value so that if timesed by all the values within the brackets would get the original answer.