Solve the equation for x:
5x – 4 – 9x
4(x - 5)

Their are 2 answers X = 5, and X = 9

x = 5 because on both sides of your equation you have (x-5) in parenthesis and you are multiplying that number by the rest of the equation.  If X = 5, then your last step on both sides of the equation will be to multiply by 0.  Hence x=5.

Now X = 9.  This solution will take a bit more work to solve first you will need to distribute both sides of your equation

5x(x-5) - to distribute this side of the equation simply multiply both numbers in the parenthesis by 5x (remember the subtraction sign means you will have to multiply by a negative number. So it becomes

(5x * x) + (5x * -5) Or 5x2 + -25x

The other side (4x + 9)(x -5) needs to be distributed.  I tend to use the FOIL method, but the box method works well too.

(4x * x) + (4x * -5) + (9 * x) + (9 x -5)

   4x2    +   -20x    +     9x    +   -45     Next add together like terms, remember you can't add an x to an x2

   4x2                     + -11x          +    -45

Okay now that we have distributed both sides I'm going to put both sides of our equation down distributed out.

5x2 + -25x = 4x2 -11x + -45

To solve for x, I need all the x's on one side of the equation, so I will use the inverse operations (remember the inverse of addition is subtraction and the inverse of multiplication is division).  Whatever I do to one side of the equation has to be done to the other side to keep it balanced.

 5x2 + -25x = 4x2 -11x + -45

-4x2            -4x2

  x2    + -25x       0   -11x + -45

         +11x         +11x

   x2 + -14x  + 0 + 0 + -45

     x2 + -14x = - 45

-31x + 176

Step-by-step explanation:

5x - 4 - 9 · 4 (x - 5)

= 5x - 4 - 36 (x-5)

= 5x - 4 - 36x + 180

= -31x + 176

Point of Interception will be (7,8/3)

Step-by-step explanation:

Point of intersection of two graph equations mean to find the value of x and y.

So,

20x - 15y = 100(1)

3x - 6y = 5(2)

Multiplying (1) with 3 and (2) with 20.

{20x - 15y = 100} * 3

= 60x - 45y = 300__(3)

&

{3x - 6y = 5} * 20

= 60x - 120y = 100_(4)

Subtracting (4) from (3),

60x - 45y = 300

60x - 120y = 100

-+-

75y = 200

y = 200/75 = 8/3

Substituting the value of y in (2)

3x - 6(8/3) = 5

3x - 16 = 5

3x = 5+16 = 21

x = 21/3 = 7

x = 7

The coordinates of interception will be x-intercept = 7 & y-intercept = 8/3.

Hope It Helped You ;)

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