Exam 24: Inequalities and Linear Programming

Find the values of $x$ for which the expression is real: $\overline{\sqrt{x^{3}+8 x^{2}-9 x}}$

Solve the inequality: $x^{2}+x<6$

A company makes two models of televisions. Model A requires 3 hours to make and $\$ 125$ in materials and yields a profit of $\$ 175$ . Model B requires 7 hours to make and $\$ 200$ in materials and yields a profit of $\$ 350$ . There are 1010 hours and $\$ 34750$ available per week to make the televisions. How many of each television model must be made each month in order to maximize profit?

Graph the inequalities: $y<8-5 x^{2}, y\geq 4 x+8$

Solve the inequality: $|4 x+3|>5$

Find the values of $x$ for which the expression is real: $\overline{\sqrt{\left(x^{2}-3 x+2\right)\left(x^{2}-x-2\right)}}$

Solve the inequality: $|5 x-21| \geq 2 x$

Solve the inequality: $|3-5 x|<2-3 x$

Label each inequality as conditional, unconditional, linear, or nonlinear: (a) $x^{2}+2>1$ (b) $x+4<2 x-3$ (c) $x^{2}-5 x+4>5$ (d) $5 x+1>x^{2}$

Solve the inequality: $2 x \leq 4 x+7<2 x+20$

Solve the inequality: $|5 x|<15$

Solve the inequality: $\left|x^{2}-5 x+5\right| \leq 1$

Graph the inequalities: $y \leq 3 x-4, y \geq 2 x+5$

Maximize the function $z=-x+2 y$ under the constraints $y \geq 4 x$ and $x+y \leq 10, x \geq 0, y \geq 0$ .

Solve the inequality: $2 x-15 \geq 5+6 x$

Write $-5 \leq x<7$ using bracket notation.

Graph the inequality on the number line: $x \leq-4$

Graph the following inequality as a ray or interval on the number line: $x>9$

Rewrite each double inequality as two separate inequalities: (c) $-1 \leq x \leq 8$ (d) $-10 \leq x<-5$

A company can make a toaster for $\$ 9.50$ and sell it for $\$ 29.75$ . Find the minimum number of toasters that must be sold for the company to make a profit if it has an overhead cost of $\$ 8100$ per week.