Compare the answers to previous questions and check whether both agree or not.

Solve the polynomial inequality and express the solution set using interval notation.

$$x^2<-4$$

Determine whether the following statements are true or false.

The quadratic equation $a x^2+b x+c=0$ can be solved by the square root method only if $b=0$.

Solve the inequality $-a x+b<-a x+c$, where $0<b<c$.

Solve the polynomial inequality and express the solution set using interval notation.

$$-x^2<-7 x$$

Solve the polynomial inequality and express the solution set using interval notation.

$$-x^2 \geq 9 x+14$$

Solve the inequality $a x+b<a x-c$, where $0<b<c$.

Determine whether the following statements are true or false.

The equation $(3 x+1)^2=16$ has the same solution set as the equation $3 x+1=4$.

Solve the polynomial inequality and express the solution set using interval notation.

$$4 x \leq x^2$$

Solve the inequality $x>-x$ mentally (without doing any algebraic manipulation).

$$\begin{aligned} 2 x^2-4 x &=3 \\ 2\left(x^2-2 x\right) &=3 \\ 2\left(x^2-2 x+1\right) &=3+1 \\ 2(x-1)^2 &=4 \\ (x-1)^2 &=2 \\ x-1 &=\pm \sqrt{2} \\ x &=1 \pm \sqrt{2} \end{aligned}$$

..

$$\begin{aligned} 16 a^2+9 &=0 \\ 16 a^2 &=-9 \\ a^2 &=-\frac{9}{16} \\ a &=\pm \sqrt{\frac{9}{16}} \\ a &=\pm \frac{3}{4} \end{aligned}$$

Solve the polynomial inequality and express the solution set using interval notation.

$$6 x^2-7 x<20$$

Budget. A woman decides to start a small business making monogrammed cocktail napkins. She can set aside $\$ 1870$ for monthly costs. Fixed costs are $\$ 1329.50$ per month and variable costs are $\$ 3.70$ per set of napkins. How many sets of napkins can she afford to make per month?