Practice section 2 of 7

For real x, prove $2x^2-x+2$ is always positive. Solve $(3x-1)/(2x^2-x+2)\ge1/x$, leaving the answer in exact form.

Find the set of values of x satisfying $(x+1)/x\ge3/(x+2)$.

Solve $x>\sqrt{16-x^2}$.

Self-Practice 3: solve $\sqrt{x}>2x$.

Solve (a) $|x-3|<4$ and (b) $|2x+1|\ge4$.

Self-Practice 4: solve $|2x+a|<5$, leaving the answer in terms of a.