91Ó°ÊÓ

Explain why the inequality \(|x|>-5\) is true for all real numbers \(x\).

Explain how the zero product property can be used to solve a polynomial equation.

Determine if the equation is linear, quadratic, or neither. If the equation is linear or quadratic, find the solution set. \(-x\left(x^{2}-5\right)+4=x^{2}+5\)

Solve the equation by using any method. \((3 x-4)^{2}=0\)

Why must the potential solutions to a radical equation be checked in the original equation?

Explain the difference between the solution sets for the following inequalities: $$|x-3| \leq 0 \text { and }|x-3|>0$$

Consider a seesaw with two children of masses \(m_{1}\) and \(m_{2}\) on either side. Suppose that the position of the fulcrum (pivot point) is labeled as the origin, \(x=0 .\) Further suppose that the position of each child relative to the origin is \(x_{1}\) and \(x_{2}\), respectively. The seesaw will be in equilibrium if \(m_{1} x_{1}+m_{2} x_{2}=0 .\) Use this equation. Find \(x_{2}\) so that the system of masses is in equilibrium. \(m_{1}=30 \mathrm{~kg}, x_{1}=-1.2 \mathrm{~m}\) and \(m_{2}=20 \mathrm{~kg}, x_{2}=?\)

Solve for the specified variable. (See Examples \(8-9)\) $$ S=\frac{n}{2}(a+d) \text { for } d $$

Explain why \(x^{2}=4\) is equivalent to the equation \(|x|=2\).

Consider the equation \(u^{m / n}=k,\) where \(m\) is an even integer and \(k\) is a positive real number. Explain why the \(\pm\) symbol is necessary in the solution set \(\left\\{\pm k^{n / m}\right\\}\).