Help with these math problems?

Solve for t : |6 − 4/7t| + 7 = 9 

Is the t supposed to be in the denominator of 4/7 or in the numerator?

The corporate profits for various U.S. industries vary from year to year. An approximate model

for profits of U.S. "communications companies" during a given year between 1990 and 1997 is

given by 

P = −3,400|x − 5.5| + 36,000 

where P is the annual profits (in millions of dollars) and x is the number of years after 1990. Use

the model to determine the years in which profits of "communication companies" were $31.5

billion ($31,500 million). 

P = −3,400|x − 5.5| + 36,000 

P - 36,000 = −3,400|x − 5.5|

(P - 36,000)/-3,400 = |x − 5.5|

(P - 36,000)/-3,400 = x − 5.5

[(P - 36,000)/-3,400] + 5.5 = x

x = [(P - 36,000)/-3,400] + 5.5

P = 31,500

x = [(31,500 - 36,000)/-3,400] + 5.5

x = [(-4,500)/-3,400] + 5.5

x = [1.323529] + 5.5

x = 1.323529 + 5.5

x = 6.823529 ≈ 7

1990 + 7 = 1997 year of profits of $31.5 billion

-(x - 5.5) = -x + 5.5 = 5.5 - x

P = −3,400(5.5 - x) + 36,000 

P - 36,000 = −3,400(5.5 - x)

(P - 36,000)/-3,400 = (5.5 - x)

(P - 36,000)/-3,400 = 5.5 - x

[(P - 36,000)/-3,400] + x = 5.5

x = 5.5 - [(P - 36,000)/-3,400]

P = 31,500

x = 5.5 - [(31,500 - 36,000)/-3,400]

x = 5.5 - [1.323529]

x = 5.5 - 1.323529

x = 4.176471 ≈ 4

1990 + 4 = 1994 year of profits of $31.5 billion

So, in the years 1994 and 1997, the communications industry

made profits of $31,500,000,000.