Solve the following equations and inequalities analytically. Support your solutions graphically. \( \begin{array}{lll}\text { (a) }|5 x+4|+2=7 & \text { (b) }|5 x+4|+2 \leq 7 & \text { (c) }|5 x+4|+2 \geq 7\end{array} \) A. The solution set is the finite set of real numbers \( \{ \) (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The solution set is the interval \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) C. The solution set is \( \varnothing \).

Solve the system by graphing each equation and finding the point of intersection. \( \begin{array}{l}y=\frac{-12}{x+4}+3 \\ y-14=(x+6)^{2} \\ x= \\ y=\end{array} \)

(c) \( 3 x^{2}-x=x^{2}-5 x+6 \)

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was \( \$ 420 \). Each envelope costs \( \$ 0.03 \) and they get paid \( \$ 0.06 \) per envelope stuffed. Let \( x \) represent the number of envelopes stuffed. (a) Express the cost \( C \) as a function of \( x \). (b) Express the revenue \( R \) as a function of \( x \). (c) Determine analytically the value of \( x \) for which revenue equals cost. (a) \( C(x)=\square \) (C in dollars) (b) \( R(x)=\square \) ( \( R \) in dollars) (c) Revenue equals cost when \( x=\square \)

1.) \( \frac{x^{3}-3 x^{2}-4 x+12}{x-3} \) 2.) \( \frac{x^{3}-2 x^{2}+7 x-1}{x^{2}+2} \)

Rationalize the Denominator: \( \frac{4+\sqrt{7}}{3+\sqrt{7}} \)