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Section 5

Solving Non-Linear Inequalities

In each of the following exercises, solve the given inequality.$$2 x-3>0$$

In each of the following exercises, solve the given inequality.$$2 x-3 \leq 0$$

In each of the following exercises, solve the given inequality.$$(x-3)(x+4) \geq 0$$

In each of the following exercises, solve the given inequality.$$(x-3)(x+4)<0$$

In each of the following exercises, solve the given inequality.$$(3 x+5)(4 x-7) \leq 0$$

In each of the following exercises, solve the given inequality.$$(3 x+5)(4 x-7)>0$$

In each of the following exercises, solve the given inequality.$$(5 x-3)(x+5) \geq 0$$

In each of the following exercises, solve the given inequality.$$(5 x-3)(x+5)<0$$

In each of the following exercises, solve the given inequality.$$(5-2 x)(x+4)>0$$

In each of the following exercises, solve the given inequality.$$(3-4 x)(2-3 x) \geq 0$$

In each of the following exercises, solve the given inequality.$$x(2 x-5) \geq 0$$

In each of the following exercises, solve the given inequality.$$x(2 x-5)<0$$

In each of the following exercises, solve the given inequality.$$(x+2)^{2}(x-3) \geq 0$$

In each of the following exercises, solve the given inequality.$$(3 x-4)^{4}(2 x-3) \leq 0$$

In each of the following exercises, solve the given inequality.$$x(x-2)(x+3) \leq 0$$

In each of the following exercises, solve the given inequality.$$(x+1)(x-2)(x+5) \geq 0$$

In each of the following exercises, solve the given inequality.$$(2 x+3)(3 x-5)(x+1) \leq 0$$

In each of the following exercises, solve the given inequality.$$x^{2}+7 x+12 \geq 0$$

In each of the following exercises, solve the given inequality.$$x^{2}-7 x+10<0$$

In each of the following exercises, solve the given inequality.$$x^{2}+x-42>0$$

In each of the following exercises, solve the given inequality.$$6 x^{2}-x-12 \leq 0$$

In each of the following exercises, solve the given inequality.$$6 x^{2}-x-12>0$$

In each of the following exercises, solve the given inequality.$$10 x^{2}+7 x-12 \geq 0$$

In each of the following exercises, solve the given inequality.$$10 x^{2}+7 x-12<0$$

In each of the following exercises, solve the given inequality.$$24 x^{2}+10 x-25 \geq 0$$

In each of the following exercises, solve the given inequality.$$24 x^{2}+10 x-25<0$$

In each of the following exercises, solve the given inequality.$$x^{3}-16 x \geq 0$$

In each of the following exercises, solve the given inequality.$$x^{3}-16 x<0$$

In each of the following exercises, solve the given inequality.$$25 x-x^{3} \leq 0$$

In each of the following exercises, solve the given inequality.$$25 x-x^{3}>0$$

In each of the following exercises, solve the given inequality.$$x^{2}-9 \leq 7$$

In each of the following exercises, solve the given inequality.$$x^{2}+4>5$$

In each of the following exercises, solve the given inequality.$$(2 x+3)(x-3) \geq 11$$

In each of the following exercises, solve the given inequality.$$(2 x+3)(x-3)<11$$

In each of the following exercises, solve the given inequality.$$(3 x-2)(2 x+3)<28$$

In each of the following exercises, solve the given inequality.$$(3 x-2)(2 x+3) \geq 28$$

In each of the following exercises, solve the given inequality.$$(4 x-5)(5 x+4) \geq-9$$

In each of the following exercises, solve the given inequality.$$(4 x-5)(5 x+4)<-9$$

In each of the following exercises, solve the given inequality.$$\frac{(x+2)(x-1)}{x-3} \leq 0$$

In each of the following exercises, solve the given inequality.$$\frac{(x+2)(x-1)}{x-3}>0$$

In each of the following exercises, solve the given inequality.$$\frac{(2 x-5)(3 x-2)}{(x-4)^{2}}>0$$

In each of the following exercises, solve the given inequality.$$\frac{(2 x-5)(3 x-2)}{(x-4)^{2}} \leq 0$$

In each of the following exercises, solve the given inequality.$$\frac{x(2 x-3)^{2}}{(x-4)^{3}} \geq 0$$

In each of the following exercises, solve the given inequality.$$\frac{x(2 x-3)^{2}}{(x-4)^{3}}<0$$

In each of the following exercises, solve the given inequality.$$\frac{10}{x-3}<2$$

In each of the following exercises, solve the given inequality.$$\frac{10}{x-3} \geq 2$$

In each of the following exercises, solve the given inequality.$$\frac{7 x}{x+3} \geq 4$$

In each of the following exercises, solve the given inequality.$$\frac{7 x}{x+3}<4$$

In each of the following exercises, solve the given inequality.$$\frac{x}{x-1} \geq \frac{3}{2}$$

In each of the following exercises, solve the given inequality.$$\frac{x}{x-1}<\frac{3}{2}$$

In each of the following exercises, solve the given inequality.$$\frac{(x-1)(x+2)}{x-3}>1$$

In each of the following exercises, solve the given inequality.$$\frac{(x-1)(x+2)}{x-3} \leq 1$$

In each of the following exercises, solve the given inequality.$$\frac{x^{2}-16}{x^{2}-25} \leq \frac{20}{11}$$

In each of the following exercises, solve the given inequality.$$\frac{3 x^{2}(x-2)(x+3)}{(3 x+4)^{4}(2 x-1)}>0$$

In each of the following exercises, solve the given inequality.$$\frac{x^{2}-16}{x^{2}-25}>\frac{20}{11}$$

In each of the following exercises, solve the given inequality.$$\frac{3 x^{2}(x-2)(x+3)}{(3 x+4)^{4}(2 x-1)} \leq 0$$

In each of the following exercises, solve the given inequality.$$\frac{5 x^{2}(4 x-7)(2 x+9)^{3}}{(x-2)^{5}(2 x+1)^{6}} \leq 0$$

In each of the following exercises, solve the given inequality.$$\frac{5 x^{2}(4 x-7)(2 x+9)^{3}}{(x-2)^{5}(2 x+1)^{6}}>0$$

In each of the following exercises, solve the given inequality.$$x^{2}-8 \leq 0$$

In each of the following exercises, solve the given inequality.$$x^{2}-8>0$$

In each of the following exercises, solve the given inequality.$$x^{2}-2 x-1<0$$

In each of the following exercises, solve the given inequality.$$x^{2}-2 x-1 \geq 0$$

In each of the following exercises, solve the given inequality.$$x^{2}-4 x-41>0$$

In each of the following exercises, solve the given inequality.$$x^{2}-4 x-41 \leq 0$$

In each of the following exercises, solve the given inequality.$$x^{2}-2 x+5<0$$

In each of the following exercises, solve the given inequality.$$x^{2}-2 x+5 \geq 0$$