Question

solve the following inequality: 4x^3+4x^2 ≤ x+1

Answer 1

\[4x^3+4x^2-x-1 ≤ 0\]\[4x^2(x+1)-(x+1) ≤ 0\]\[(4x^2-1)(x+1) ≤ 0\]

Answer 2

\[4x^2-1=0\]\[4x^2=1\]\[x^2=1/4\]\[x=\pm 1/2\]

\[x+1=0\] \[ x=-1\]

Sub in values either side to determine the inequality.

\[x \le -1\] \[-1/2 \le x\le 1/2\]