Deck 2: Equations, Inequalities, and Problem Solving

Question 1

Determine whether each number is a solution of the given equation

--4; x - 16 = 20

Answer 1

-4 is not a solution

Question 2

Determine whether each number is a solution of the given equation
--1; 3x - 1 = 5x + 1

Answer 2

-1 is a solution

Question 3

Solve each equation and check.
--(x/2) = 14

Answer 3

{-28}

Question 4

Solve each equation and check.
-3x - 5 = 7

Question 5

Solve each equation and check.
-0.2x - 0.3 = 1.1

Question 6

Solve each equation and check.
-7y + 1 = 6y - 1

Question 7

Solve each equation and check.
-2 + 5x + 3 = 3 + 2x - 4

Question 8

Solve each equation and check.
-3(x - 5) = 12

Question 9

Solve each equation and check.
-2(2x - 1) = 5(x + 2) + x

Question 10

Solve each equation and check.
-0.6(x - 1) = 2(0.4x + 0.7)

Question 11

Solve each equation and check.
- $\frac{3x}{8}-\frac{x}{2} = \frac{3x}{4}-14$

Question 12

Solve each equation and check.
- $\frac{n}{2}-\frac{n}{3} = 1-\frac{n}{6}$

Question 13

Solve each equation and check.
-0.07x + 0.11x = 3.6

Question 14

Solve each equation and check.
--3(2n - 1) - n = -4(n - 5)

Question 15

Solve each equation and check.
- $\frac{x+2}{4}+\frac{x-3}{8} = 1$

Question 16

Solve each equation and check. Some equations are identities and some are contradictions
-2(2x - 9) = x + 3(x - 6)

Question 17

Solve each equation and check. Some equations are identities and some are contradictions
-3(x + 2) = 2(x + 4) + x + 1

Question 18

Solve each equation and check. Some equations are identities and some are contradictions
-5x + 8 = 4(x + 2)

Question 19

Solve each equation and check. Some equations are identities and some are contradictions
-4(x - 3) = 8(x - 2) - 4x

Question 20

Solve each equation and check. Some equations are identities and some are contradictions
-7(x + 1) + 3 = 3x + 4(x + 2) + 2

Question 21

Solve
-Fifteen subtracted from 3 times a number is 27. Find the number.

Question 22

Solve
-One number is 9 more than another number. The sum of the numbers is 17. Find the numbers.

Question 23

Solve
-Find 40% of 75.

Question 24

Solve
-Find 24% of 16.

Question 25

Solve
-Caitlin's total annual income last year was $42,000. If 12% of her income was from preparing income taxes in March and April, how much did she earn preparing taxes?

Question 26

Solve
-If 23% of 120,000 registered voters in an area turn out to vote, how many people in the area voted?

Question 27

Solve
-Central State estimates that 18% of its graduates are education majors. If 1700 seniors graduate next year, about how many are expected to be education majors?

Question 28

Solve
-Rachel always deposits 15% of her paycheck in her savings account. If her paycheck is $1020, what will she deposit into savings?

Question 29

Solve
-Hobart planted wheat on 24 acres more than his brother. Together the two men planted 320 acres of wheat. How many acres did each plant?

Question 30

Solve
-Tanissa paid $1431 for a computer after tax. If the tax rate is 6%, find the price of the computer before taxes.

Question 31

Solve
-The length of a rectangular calf pen is 20 feet more than the width. Find the dimensions of the pen if 200 feet of fencing is required for the perimeter of the pen.

Question 32

Solve
-The lengths of the sides of a triangle are consecutive integers. Find the lengths of the sides of the triangle if the perimeter is 111 cm.

Question 33

Solve
-In the firs year Honshu paid 24% of his loan. If the original amount of the loan was $20,000, what was the balance of the loan at the end of the first year?

Question 34

Solve
-Jamil received a 3.5% raise. This increased his annual salary by $910. What is his new annual salary?

Question 35

Solve
-Shade Tree Used Cars is selling a car for $7500. This amount is $1500 less than 3 times the cost of the car. Find the cost of the car.

Question 36

Solve
-A triangle has sides measuring 2x ft, 3.5x ft, and (3x + 2) ft. It's perimeter is 104 ft. Find the measures of the sides.

Question 37

Solve
-One of two supplementary angles is 4 $^\circ$ more than on third of the other angle. Find the measures of the angles.

Question 38

Solve
-The width of a rectangular playground is 5 feet more than half the length. The perimeter of the playground is 400 feet. Find the length and width.

Question 39

Solve
-A 20-foot long board is to be cut into two pieces so that the length of the smaller piece is two-thirds of the length of the longer piece. Find the lengths of the two pieces.

Question 40

Solve
-The numbers of accidents at Beam Lumber has increased by 40% since last year. There were 12 accidents last year. How many accidents were there this year? Round to the nearest whole number if necessary.

Question 41

Solve each equation for the specified variable.
-A = lw for w

Question 42

Solve each equation for the specified variable.
-C = $\pi$ D for D

Question 43

Solve each equation for the specified variable.
- $A = \pi{r}^2 + \pi{r}S for S$

Question 44

Solve each equation for the specified variable.
-4x - 3y = 12 for y

Question 45

Solve each equation for the specified variable.
- $A = \frac{1}{2}h(b_1 + b_2) for h$

Question 46

Solve each equation for the specified variable.
-C = 3.5n + 10 for n

Question 47

Solve each equation for the specified variable.
- $\frac{1}{a} + \frac{1}{b} = \frac{1}{c} for c$

Question 48

A principal of $8000 is invested in an account paying an annual percentage rate of 5%. Find the amount in the account after 2 years if then account is compounded n times a year.
-n = 4

Question 49

A principal of $8000 is invested in an account paying an annual percentage rate of 5%. Find the amount in the account after 2 years if then account is compounded n times a year.
-n = 12

Question 50

Solve.
-A record low temperature for Honolulu, Hawaii is 53 $^\circ$ F. Write 53 $^\circ$ F as degrees Celsius. Use the formula $C = \frac{9}{5}(F - 32)$ . Round to the nearest degree.

Question 51

Solve.
-It is 470 miles from Oklahoma City, Oklahoma to Memphis, Tennessee. Find how long it takes to drive round-trip if the average speed is 65 mph. Round to the nearest minute.

Question 52

Solve.
-A package of vinyl floor tiles contains 45 on-foot-square tiles. Find how many packages should be bought to cover the rectangular floor of an outlet store that is 120 feet by 90 feet.

Question 53

Solve.
-Find the volume of a ball with radius 6 inches. Use the formula $V = \frac{4}{3}\pi{r}^3$ . Round to the nearest whole number.

Question 54

Solve.
-A gallon of paint can cover 400 square feet. To the nearest half gallon, find how much paint will be needed to paint two coats on the walls and ceiling of a room that is 20 feet long, 18 feet wide, and 8 feet high.

Question 55

Solve.
-Jordan wants to collect rainwater in a cylindrical barrel that has a diameter of 3 feet and height of 5 feet. How much water could it hold in cubic feet? Use the formula $V = \pi{r}^2h$ . Round to two decimal places.

Question 56

Solve.
-Jonna would like to have $30,000 saved for her daughter's college education. If she invests $10,000 in an account paying 8% interest compounded quarterly, will she reach her goal in 15 years?

Question 57

Solve.
-Michaela can have unlimited on-line services for a flat fee of $20 per month or limited access for 10¢ per minute. Find the amount of time on-line for which the unlimited access plan costs the same as the limitedaccess plan.

Question 58

Solve.
-Sally has scores of 88, 92, 80, and 96. Find the score she must make on the next exam to have an average of 90.

Question 59

Solve.
-A company finds that the cost C to produce x items is C = 10,025 + 1.09x, while the revenue is R = 6.42x. Find the break-even point. (Cost equals revenue at the breakeven point.)

Question 60

Solve.
-The cost of renting a car at EZ Rentals is $35 a day plus 20 cents per mile. How far can Nguyen drive on $80?

Question 61

Graph the solution set of each inequality on a number line and then write it in interval notation.
- $\{x|x \geq -8\}$

Question 62

Graph the solution set of each inequality on a number line and then write it in interval notation.
- $\{x|3 < x\}$

Question 63

Graph the solution set of each inequality on a number line and then write it in interval notation.
- $\{x|-1 \leq x < 4\}$

Question 64

Graph the solution set of each inequality on a number line and then write it in interval notation.
- $\{x|-4 < x < -1\}$

Question 65

Solve. Graph the solution set and write it in interval notation.
-x - 4 $\geq$ -7

Question 66

Solve. Graph the solution set and write it in interval notation.
-3x < 2x - 6

Question 67

Solve. Graph the solution set and write it in interval notation.
-9x - 5 $\leq$ 8x + 3

Question 68

Solve. Graph the solution set and write it in interval notation.
- $\frac{2}{5}x > 4$

Question 69

Solve. Graph the solution set and write it in interval notation.
-8x $\leq$ 2.08

Question 70

Solve. Graph the solution set and write it in interval notation.
--x $\geq$ -9

Question 71

Solve. Write the solution using interval notation.
--4x + 7 < -9

Question 72

Solve. Write the solution using interval notation.
-3x - 5 > 6x + 4

Question 73

Solve. Write the solution using interval notation.
-2(x + 1) $\leq$ 3(x - 8)

Question 74

Solve. Write the solution using interval notation.
- $\frac{2}{3}(x-6) \geq \frac{4}{5}(x-10)$

Question 75

Solve. Write the solution using interval notation.
-8x - 7(1 + x) $\geq$ 3(x - 2) + 2x

Question 76

Solve. Write the solution using interval notation.
-1.5 + 0.2x < 0.4x - 0.7

Question 77

Solve. Write the solution using interval notation.
- $\frac{2}{3}-\frac{4}{5}x \geq \frac{3}{10}x + \frac{1}{5}$

Question 78

Solve.
-A custodian must move a shipment of books from the first floor to the sixth floor. The elevator's weight limit is 900 pounds. If the custodian weighs 160 pounds and each box of books weighs 37 pounds, find the maximum number of boxes the custodian can move on the elevator at one time.

Question 79

Solve.
-To receive an A in a course, Twan must have an average of 90 or above. If Twan's first four exam grades are 96, 90, 87, and 95, what is the minimum grade Twan can receive on the last exam to get an A in the course?

Question 80

Solve.
-For Brooke's cookie company to make a profit, her revenue R must be greater than her cost C. Her weekly cost equation is C = 1.7x + 1525 and her weekly revenue equation is R = 4.2x, where x is the number of packages o cookies produced and sold in a week. How many packages of cookies must Brooke's company produce and sell in a week to make a profit?