Problem: If x/42=4x/2\dfrac{x / 4}{2}=\dfrac{4}{x / 2}2x/4=x/24 then x=x=x=
Answer Choices:
A. ±1/2\pm 1 / 2±1/2
B. ±1\pm 1±1
C. ±2\pm 2±2
D. ±4\pm 4±4
E. ±8\pm 8±8
Solution:
Multiply both sides of the given equation by 2⋅x22 \cdot \dfrac{x}{2}2⋅2x to obtain x28=8\dfrac{x^{2}}{8}=88x2=8. Thus x2=82x^{2}=8^{2}x2=82, or x=±8x= \pm 8x=±8.