Question

In the figure, segment RD bisect segment DE at S. Given that DS=4x+12 and SE=8x-8, find the value of x.

Answer 1

`x = 5`

Explanation:

DS = 4x + 12

SE = 8x - 8

Since segment RS bisects segment DE, it implies that the two segments created, segments DS and SE, are congruent. Therefore:

`4x + 12 = 8x - 8`

Solve for x

`4x + 12 - 8x = 8x - 8 - 8x` (Subtraction property of equality)

`-4x + 12 = - 8`

`-4x + 12 - 12 = - 8 - 12` (subtraction property of equality)

`-4x = - 20`

`(-4x)/(-4) = (-20)/(-4)`

`x = 5`