Step-by-step explanation:
the error:
it is stated that
subtract (5x)/(x+7) from both sides

multiply both sides by x + 7
7(x+7) = 49x
7x + 49 = 49x
subtract 7x from both sides to isolate x and its coefficient
49 = 42x
thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must <em>always </em>be true, so this is wrong
the solution:
we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x by 1.
anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.
(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get

substitute this for 7/x in our original problem

(2/5) / 1 = x / (3/4).....2/5 cups to 1 pie = x cups to 3/4 pie
cross multiply
(1)(x) = (2/5)(3/4)
x = 6/20 which reduces to 3/10 cups <==
Answer:
x = 9
Step-by-step explanation:
6x = 4x + 18
6x - 4x = 18
2x = 18
x = 9
Answer:
a) 22:24 simplified the answer is 11:12
b) 21:81 simplified the answer is 7:27
Step-by-step explanation:
not sure how you were taught but those could also be
a)
or simplified the answer is 
b)
or simplified the answer is 