Answer:
[tex] x = 5 [/tex]
Step-by-step 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:
[tex] 4x + 12 = 8x - 8 [/tex]
Solve for x
[tex] 4x + 12 - 8x = 8x - 8 - 8x [/tex] (Subtraction property of equality)
[tex] -4x + 12 = - 8 [/tex]
[tex] -4x + 12 - 12 = - 8 - 12 [/tex] (subtraction property of equality)
[tex] -4x = - 20 [/tex]
[tex] \frac{-4x}{-4} = \frac{-20}{-4} [/tex]
[tex] x = 5 [/tex]
