Deck 8: Section 2: More on Inequalities

Question 1

Graph the solution to the absolute value inequality.

Answer 1

Question 2

Write as a single interval if possible: [-1, $\infty$ ) $\cup$ (4, $\infty$ )

Answer 2

[-1, $\infty$ )

Question 3

Write an absolute value inequality whose solution set is given by the graph.

Answer 3

|x| $\ge$ 2

Question 4

Graph the solution set of the inequality .

Question 5

Solve: |x - 5| = 3

Question 6

Determine whether the absolute value inequality is equivalent to the inequality following it:
|-2 - x| < 14, -2 - x < 14 and -(-2 - x) < 14

Question 7

Determine whether or not the solution set to the inequality is the empty set.

Question 8

Solve: 12 - |-13 - x| = 2

Question 9

Trisha needs to adjust her cholesterol level to a target value of 170. She recalls that her cholesterol level differed from her target value by 6 units, but does not recall whether she is above or below the target value. Use an absolute value equation to find the possible values for Trisha's cholesterol level.

Question 10

Graph the solution to the absolute value inequality.

Question 11

Graph the solution to the compound inequality.

Question 12

Let . Evaluate each expression.
a) R(3, 4) b) R(8, 3) c) R(5, 0)

Question 13

Graph the solution set for the following system of inequalities and identify each vertex of the region.
x $\ge$ 0, y $\ge$ 0
2x + y $\ge$ 4
2x + 3y $\ge$ 7

Question 14

Determine if the compound inequality is true: 10 $\le$ 10 and 10 > 0

Question 15

Solve the inequality and write the solution set in interval notation.
5 < |x| - 10

Question 16

Kara works at a bakery and can prepare a birthday cake in 4 hours. It takes her 5 hours to prepare a wedding cake. Kara works a 40-hour week and she must bake more wedding cakes than birthday cakes. Draw a graph that illustrates the number of each type of cake Kara can bake per week.

Question 17

Professor Jackson gives only a mid-term exam and a final exam. The semester average is computed by taking of the mid-term exam score plus of the final exam score. To get a C, Birgit must have a semester average between 70 and 79 inclusive. If Birgit scored 65 on the mid-term exam, what range of scores on the final exam would give her a C ?

Question 18

Determine which of the ordered pairs (3, 2), (-3, 4), (-1, -5), and (1, -6) satisfy the compound inequality.
y < -x + 2 or y > 2x - 4

Question 19

Graph the solution to the absolute value inequality.

Question 20

Write as a single interval if possible: (-9, $\infty$ ) $\cup$ [13, $\infty$ )

Question 21

Carla wants to purchase insurance for her landscaping business. She determines that she needs at least $137,500 of property coverage and at least $137,800 of liability coverage. In order to gain this amount of coverage, she can purchase any combination of insurance plans A and B from two different insurance companies. For each dollar she spends on Plan A, she gets $250 of property coverage and $280 of liability coverage. Plan B provides $290 of property coverage and $260 of liability coverage for each dollar of premium paid. How much should she spend on each plan to minimize her insurance cost?

Question 22

The Belew's Creek Volunteer Fire Department is having a community chicken dinner in order to raise funds. Patrons have a choice between two sizes of dinners. The small dinner costs $2.50 and comes with one piece of chicken and two rolls. The large dinner costs $4.00 and comes with two pieces of chicken and three rolls. The department has a total of 568 rolls and 300 pieces of chicken. How many of each type of dinners need to be sold to maximize the fire department's revenue?