Question

I need helpp this is geometry

Answer 1

x = 8 , AB = BC = 1

Explanation:

we require

AB = BC , that is

`(3)/(4)` x - 5 =
`(9)/(4)` x - 17

multiply through by 4 to clear the fractions

3x - 20 = 9x - 68 ( subtract 9x from both sides )

- 6x - 20 = - 68 ( add 20 to both sides )

- 6x = - 48 ( divide both sides by - 6 )

x = 8

Then

AB =
`(3)/(4)` × 8 - 5 = 6 - 5 = 1

BC =
`(9)/(4)` × 8 - 17 = 18 - 17 = 1

so AB = BC

Answer 2

x = 8

AB = 1

BC = 1

Explanation:

AB = BC when

`(3)/(4)x - 5 = (9)/(4)x - 17`

In the above equation bring all the x terms to the left and the constants to the right as follows

• Add 5 on both sides:
  
  `(3)/(4)x - 5 + 5 = (9)/(4)x - 17 + 5\\\\(3)/(4)x = (9)/(4)x - 12 \\\\\\`
  
• Subtract
  `(9)/(4)` on both sides:
  
  `(3)/(4)x - (9)/(4)x = - 12 \\\\\\`
  
• 
  `-(6)/(4)x = -12\\\\\\-(3)/(2)x = -12\\\\`
  
• Multiply both sides by
  `-(2)/(3)`:
  
  `-(2)/(3) * -(3)/(2)x = -(2)/(3) * -12\\\\x = 8\\\\\\`

Since x = 8 we can solve for the lengths of both segments by plugging in the value in the two expressions

`AB = (3)/(4) * 8 - 5\\\\AB = 6 - 5 = 1\\\\BC = (9)/(4) * 8 - 17\\\\BC = 18 - 17 = 1\\\\`

So AB = BC = 1