91Ó°ÊÓ

Complete each statement using the word intersection or the word union. The _____ of two sets is the set of all elements that are in either set or in both sets.

Find the maximum and the minimum values of each objective function and the values of \(x\) and \(y\) at which they occur. \(P=8 x-y+20\) subject to \(6 x+8 y \leq 48\) \(0 \leq y \leq 4\) \(0 \leq x \leq 7\)

Solve. Write the answer using set notation. $$ |x-2|=6 $$

Graph and write interval notation for each compound inequality. $$ 0 \leq y \leq 5 $$

Simplify. Do not leave negative exponents in your answer. $$ \left(\frac{4 c^{2} d}{6 c d^{4}}\right)^{-1} $$

Solve. Then graph. Write the solution set using both set-builder notation and interval notation. $$ -0.5 x<-30 $$

Graph each system of inequalities. Find the coordinates of any vertices formed. $$ \begin{aligned} &x-y \leq 2\\\ &x+2 y \geq 8\\\ &y \leq 4 \end{aligned} $$

Graph each system of inequalities. Find the coordinates of any vertices formed. $$ \begin{aligned} &8 x+5 y \leq 40\\\ &x+2 y \leq 8\\\ &x \geq 0\\\ &y \geq 0 \end{aligned} $$

Solve. Write the solution set using both set-builder notation and interval notation. $$ 8 x-3(3 x+2)-5 \geq 3(x+4)-2 x $$

Solve. Write the solution set using both set-builder notation and interval notation. $$ 13-(2 c+2) \geq 2(c+2)+3 c $$