Question

In the trapezoid below x = ?

Answer 1

x = 12

Explanation:

The mid segment is half the sum of the 2 parallel bases, that is

5x - 20 =
`(2x+6+4x+2)/(2)`

5x - 20 =
`(6x+8)/(2)` ( multiply both sides by 2 to clear the fraction )

10x - 40 = 6x + 8 ( subtract 6x from both sides )

4x - 40 = 8 ( add 40 to both sides )

4x = 48 ( divide both sides by 4 )

x = 12

Answer 2

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`((2x + 6) + (4x + 2))/(2) = 5x - 20 \\`

`(6x + 8)/(2) = 5x - 20 \\`

`(2(3x + 4))/(2) = 5x - 20 \\`

`3x + 4 = 5x - 20`

Subtract sides 4

`3x + 4 - 4 = 5x - 20 - 4`

`3x = 5x - 24`

Subtract sides 5x

`- 5x + 3x = - 5x + 5x - 24`

`- 2x = - 24`

Negatives simplifies

`2x = 24`

Divided sides by 2

`(2)/(2) x = (24)/(2) \\`

`x = 12`

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