Practice section 3 of 7

Solve $|1-2x|>|x+3|$.

Without using a calculator, solve $(x^2+2x+8)/[(x+3)(x-2)]<0$.

Hence solve $(x^2+2|x|+8)/[(|x|+3)(|x|-2)]<0$.

Sketch $y=2/(x+1)$. By sketching another suitable graph, solve $4/(x+1)\le2|x|$.

Hence solve $4/(\ln x+1)\le2|\ln x|$.

Without using a calculator, find the solution sets of the following inequalities.

(a) $\dfrac{(x+2)^2}{x^2-1}\leq0$,

(b) $\dfrac{x^2+2x+2}{x^2-x+2}<0$,

(c) $\dfrac1{(x-1)(x-3)}<-1$,

(d) $1\leq\dfrac1{3x-2}<3$.

Without using a calculator, solve the following inequalities.

(a) $|2x-3|<11$,

(b) $|x^2-8|\geq4$.

Solve $\left|\dfrac{x}{2}+3\right|>3-x^2$. Hence, solve $\left|\dfrac{e^x}{2}-3\right|>3-e^{2x}$.