Respuesta :

semsee45

Answer:

x = 9

Step-by-step explanation:

If ABCD is a parallelogram, then 6x = 7x - 9

as the point of intersection of the 2 diagonals is the midpoint of AC

6x = 7x - 9

Subtract 6x from both sides:

⇒ 0 = x - 9

Add 9 to both sides:

⇒ 9 = x

Solution:

We know that:

  • [tex]\frac{AC}{2} = 6x[/tex]

This means that:

  • [tex]AC = (6x)(2) = 12x[/tex]
  • [tex]AC = 12x = 6x + 7x - 9[/tex]

Step-by step calculations:

Simplify the RHS:

  • [tex]12x = 6x + 7x - 9[/tex]
  • => [tex]12x = 13x - 9[/tex]

Subtract 13x both sides:

  • => [tex]-13x + 12x = 13x -13x - 9[/tex]
  • => [tex]-x = -9[/tex]

Divide -1 both sides:

  • => [tex]-x = -9[/tex]
  • => [tex]\frac{-x}{-1} = \frac{-9}{-1}[/tex]
  • => [tex]x = 9[/tex]

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