How to solve this equation with REAL numbers?

Question

4 - (4x)/(x^2+1) = 1 + sin(πx/2)

Answer 1

3 - 4x/(x^2+1) = sin(pix/2)

pix/2 = sin^-1(3-4x/(x^2+1)

-1 </= 3 - 4x/(x^2+1) </= +1

-4 </= -4x/(x^2+1) </= -2

divide by -4, reverse the inequalities when multiplying or dividing by a negative number

1 >/= 1/(x^2 +1) >/= 1/2

x^2 + 1 >/= 1

x^2 >/= 0

x^2 + 1 </=2

x^2 </= 1

-1 </= x </= 1