Exam 4: Inequalities and Problem Solving

Solve. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $1.15. After that, each additional minute or portion of a minute of that call costs $0.20. Use an inequality to find the number of minutes one can call long distance for $2.15.

Solve. -When a number is subtracted from -7, the absolute value of the difference is more than 3. Use interval notation to express the set of all numbers that satisfy this condition.

Find the solution set for the equation. - $| 4 x + 9 | = | x - 4 |$

Solve. Use interval notation to express the range. -The formula for converting Celsius temperature, $C$ , to Fahrenheit temperature, $F$ , is $\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \text {. }$ If Fahrenheit temperature ranges from $41 ^ { \circ }$ to $176 ^ { \circ }$ , inclusive, what is the range for the Celsius temperature?

Find the solution set for the equation. - $| x | = 6$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $- 4 x + 1 \geq 9$ or $6 x + 3 \geq - 21$

Graph the inequality. -

Solve. Use interval notation to express the range. -The formula C = 0.5x + 18 represents the estimated future cost of yearly attendance at State University, where C is the cost in thousands of dollars x years after 2010. Use a compound inequality to determine in which years attendance costs will range from 22 to 24 thousand dollars.

Find the solution set for the equation. - $\left| \frac { 2 x + 5 } { 3 } \right| = 3$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 3 } \leq 1$

Solve. -Chi is assigned to construct a triangle with the measure b of the base and the measure h of the height differing by no more than 0.2 centimeters. Express the relationship between b and h as an inequality involving absolute value.

Solve. -Greg is opening a car wash. He estimates his cost equation as C = 8000 + 0.08x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit.

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $17 \leq \frac { 9 x } { 7 } + 8 < 26$

Solve. -The radius r of a plastic tube used in manufacturing a child's toy must not differ from the standard s by more than 5 millimeters. The manufacturing engineers express this as |r - s| ≤5. If the standard s is 33, solve the inequality for the radius r. Express the answer in set-builder notation.

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $-31 \leq-4 x-3<-15$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $- 4 x \leq - 12$ or $4 x > 12 x - 8$

Find the intersection of the sets. - $\{ - 4,0,2,5 \} \cap \{ 2,5,8 \}$

Graph the inequality. - $y \geq - \frac { 1 } { 2 } x$

Solve and graph the solution set on a number line. - $5 + \left| 1 - \frac { x } { 2 } \right| \geq 8$

Solve and graph the solution set on a number line. - $2 + \left| 1 - \frac { x } { 2 } \right| \leq 5$