First, we have to get the variable to one side of the equation, which can be done with simple subtraction.
4x -3 (-6x) = 6x + 9 (-6x)
-2x -3 = 9
now just solve as a regular equation:
-2x - 3 = 9
-2x = 12
x = -6
so, x is equal to -6
The answer is A) A relation includes both domain and range
5) it is a function because each x value only has one y value. Domain: (-infinity,infinity) range: [0,infinity)
6) it is a function. Domain: (-infinity, infinity) Range: [3,3]
7) it is a function. Domain: (-infinity, infinity) range: (-infinity, infinity)
8) it is a function. Domain: [0, infinity) range: [0, infinity)
You have a lot of questions here, I will help with the first three:
Factor:
4x^2 + 20x Factor out a 4x
4x(x + 5)
x^2 + 9x + 8 You have to work backwards with FOIL here
(x + 1)(x + 8)
Solve:
4r^2 - 16 = 84
4r^2 = 100
r^2 = 25
r = 5 or r = -5
Answers:________________________________________________Question 1) The domain of the function is:
"
x = {x | x ≠ } " .
________________________________________________Question 2) The domain of the function is:
"
x = {x | x ≠ -7, -1 ]} " . "
________________________________________________Explanations:________________________________________________Explanation for "Question 1" ;
The denominator cannot equal "0".
So; set the "denominator" equal to "0" ; as follows:
→ 2x - 1 = 0 ;
Add "1" to each side of the equation:
2x - 1 + 1 = 0 + 1 ;
2x = 1 ;
Divide each side of the equation by "2" ;
2x/2 = 1/2 ;
to get: "x = 1/2" .
________________________________________________________Answer: The domain is: "
{x | x ≠ } " .
________________________________________________________
Explanation for: "Question 2" )________________________________________________________The denominator cannot equal "0";
→ {since one cannot "divide by 0" } ;
→ So; set the "denominator" equal to "0" ;
→ (x² + 8x + 7) = 0 ; Factor:
___________________________________________(x + 7) (x + 1) = 0 ;
x = -7 ; x = -1 ;
_____________________________________________Answer: _____________________________________________The domain of the function is:_____________________________________________ "
x = {x | x ≠ -7, -1 ]} " .
_____________________________________________