Title: Unit 5 Quiz
Course: Technical Math for Industry

Q: Solve the inequality for m.
A: (a choice with no text)
If wrong: Incorrect. Did you move all the non-variable terms to one side? Check your solution to see if it makes the inequality a true statement.
If wrong: Incorrect. Did you move all the non-variable terms to one side? Check your solution to see if it makes the inequality a true statement.
If wrong: Incorrect. Did you move all the non-variable terms to one side? Check your solution to see if it makes the inequality a true statement.
If right: Correct. Since solving the inequality requires you to isolate the variable m, use the Properties of Inequality to work out that .

Q: Which one of the following values of h is a solution for the inequality ?
A: (a choice with no text)
If wrong: Incorrect. Plug in all the answer choices. Which one causes the inequality to be true?
If wrong: Incorrect. Plug in all the answer choices. Which one causes the inequality to be true?
If wrong: Incorrect. Plug in all the answer choices. Which one causes the inequality to be true?
If right: Correct. To find solutions to the inequality, isolate the variable h to get , meaning a number greater than or equal to 12 will satisfy the inequality.

Q: Solve the inequality for the variable x.
A: (a choice with no text)
If wrong: Incorrect. Did you move all the non-variable terms to one side and use the correct mathematical operation(s) to simplify your inequality? Are you using the right inequality?
If wrong: Incorrect. Did you move all the non-variable terms to one side and use the correct mathematical operation(s) to simplify your inequality? Are you using the right inequality?
If right: Correct. To solve the inequality, isolate the variable x by adding 2 to both sides and then multiplying both sides by .
If wrong: Incorrect. Did you move all the non-variable terms to one side and use the correct mathematical operation(s) to simplify your inequality? Are you using the right inequality?

Q: The forecaster on TV said, "It's a scorcher! Right now it's 90 degrees but the temperature will fluctuate at least 12 degrees by 3 PM. We'll tell you if we're getting hotter or colder in a minute!”

What is the range of possible temperatures it could be at 3 PM?
- Between 78 and 102 degrees. (Incorrect. If the temperature gets exactly 12 degrees warmer or cooler, what two temperatures could it be at 3 PM? What does it mean if the temperature difference is at least 12 degrees?)
- Cooler than 102 degrees. (Incorrect. If the temperature gets exactly 12 degrees warmer or cooler, what two temperatures could it be at 3 PM? What does it mean if the temperature difference is at least 12 degrees?)
- Hotter than 78 degrees. (Incorrect. If the temperature gets exactly 12 degrees warmer or cooler, what two temperatures could it be at 3 PM? What does it mean if the temperature difference is at least 12 degrees?)
- Cooler than 78 degrees or hotter than 102 degrees. (Correct. Since the temperature is forecast to be at least 12 degrees different, it could be either at least 12 degrees warmer or colder. This menas that it could be less than 78 degrees or more than 102 degrees.)
A: Cooler than 78 degrees or hotter than 102 degrees.

Q: If the inequality was graphed on a number line, which of the following would you expect to see?
- A closed circle at -3, an open circle at 3, and a line between them. (Correct. The graph of the inequality will consist of all the points between -3 (inclusive) and 3 (exclusive).)
- An open circle at -3 with a line towards negative infinity, and a closed circle at 3 with a line towards infinity. (Incorrect. Think about some of the possible values for x that make this inequality true. Where do these values fall on the number line? Do they include or exclude the points -3 and 3?)
- An open circle at -3, a closed circle at 3, and a line between them. (Incorrect. Think about some of the possible values for x that make this inequality true. Where do these values fall on the number line? Do they include or exclude the points -3 and 3?)
- A closed circle at -3 with a line towards negative infinity, and an open circle at 3 with a line towards infinity. (Incorrect. Think about some of the possible values for x that make this inequality true. Where do these values fall on the number line? Do they include or exclude the points -3 and 3?)
A: A closed circle at -3, an open circle at 3, and a line between them.

Q: Solve the inequality .
- or (Incorrect. The distance between x and zero has to be greater than 1. Pick numbers that satisfy this requirement and then fit those numbers to an answer choice.)
- or (Incorrect. The distance between x and zero has to be greater than 1. Pick numbers that satisfy this requirement and then fit those numbers to an answer choice.)
- or (Correct. Create the two inequalities and . Solve the latter inequality by multiplying both sides by -1 and flipping the sign.)
- or (Incorrect. The distance between x and zero has to be greater than 1. Pick numbers that satisfy this requirement and then fit those numbers to an answer choice.)
A: or

Q: Solve the inequality .
- or (Correct. Isolate the absolute value by subtracting 5 from both sides of the inequality, followed by dividing by 2. Then create and solve two separate inequalities.)
A: or
If wrong: Incorrect. Isolate the absolute value by subtracting 5 from both sides and then dividing both sides by two. Now that it’s isolated, how do you get rid of the absolute value?
If wrong: Incorrect. Isolate the absolute value by subtracting 5 from both sides and then dividing both sides by two. Now that it’s isolated, how do you get rid of the absolute value?
If wrong: Incorrect. Isolate the absolute value by subtracting 5 from both sides and then dividing both sides by two. Now that it’s isolated, how do you get rid of the absolute value?

Q: Solve the inequality .
A: (a choice with no text)
If right: Correct. Once the absolute value is isolated and the two inequalities are created, add 3 to both sides.
If wrong: Incorrect. First, make sure you’ve gotten alone by subtracting the 5 and dividing by 2. Recall that you need to create two separate inequalities and then solve them both.
If wrong: Incorrect. First, make sure you’ve gotten alone by subtracting the 5 and dividing by 2. Recall that you need to create two separate inequalities and then solve them both.
If wrong: Incorrect. First, make sure you’ve gotten alone by subtracting the 5 and dividing by 2. Recall that you need to create two separate inequalities and then solve them both.

Q: Which plot represents the solution to  ?
A: (a choice with no text)
If wrong: Incorrect. Isolate the absolute value and generate some values for x that cause the inequality to be true. Match these up with the number lines, making sure to check the boundary values (open/closed circles).
If wrong: Incorrect. Isolate the absolute value and generate some values for x that cause the inequality to be true. Match these up with the number lines, making sure to check the boundary values (open/closed circles).
If right: Correct. The solution is or , which is represented by two open circles and arrows from each circle heading towards negative infinity and infinity, with no shading in between the circles.
If wrong: Incorrect. Isolate the absolute value and generate some values for x that cause the inequality to be true. Match these up with the number lines, making sure to check the boundary values (open/closed circles).

Q: Select the plot below that is the best representation for the inequality .
A: (a choice with no text)
If wrong: Incorrect. What values of x make this inequality true? They must be between -3 and 3 or equal to 3. Does your line represent all these numbers and no others?
If wrong: Incorrect. What values of x make this inequality true? They must be between -3 and 3 or equal to 3. Does your line represent all these numbers and no others?
If right: Correct. There should be a closed circle at -3, an open circle at 3, and the line in between them should be shaded.
If wrong: Incorrect. What values of x make this inequality true? They must be between -3 and 3 or equal to 3. Does your line represent all these numbers and no others?

Q: Choose which inequality accurately represents the following statement: "Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."
- 45 MPH Bobby’s speed on the highway 65 MPH (Incorrect. Can Bobby go exactly 45 MPH? What about 65 MPH? Look at the inequality signs in this problem and try it again.)
- 45 MPH Bobby’s speed on the highway 65 MPH (Incorrect. Can Bobby go exactly 45 MPH? What about 65 MPH? Look at the inequality signs in this problem and try it again.)
- 45 MPH Bobby’s speed on the highway 65 MPH (Incorrect. Can Bobby go exactly 45 MPH? What about 65 MPH? Look at the inequality signs in this problem and try it again.)
- 45 MPH Bobby’s speed on the highway 65 MPH (Correct. Bobby is restricted from going lower than 45 MPH or higher than 65 MPH, but can go both of those speeds and be obeying the speed limit.)
A: 45 MPH Bobby’s speed on the highway 65 MPH

Q: Consider the problem: Jasmine wants to buy a brand new pair of headphones that cost $99. While she already has $40 saved up, she is planning on working at a local grocery store for $8 an hour to make up the extra cash.

Which of the following inequalities will help her determine values of , the number of hours that Jasmine can work so she can afford the new headphones?
- $40 $8 $99 (Incorrect. The amount of money that Jasmine can earn for hours of work is $8 . This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($99). Which inequality best represents this situation?)
- $40 $8 $99 (Correct. The amount of money that Jasmine can earn for hours of work is $8. This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($99). This implies the inequality $40 $8 $99.)
- $40 $8 $99 (Incorrect. The amount of money that Jasmine can earn for hours of work is $8 . This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($99). Which inequality best represents this situation?)
- $8 $99 (Incorrect. The amount of money that Jasmine can earn for hours of work is $8 . This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($99). Which inequality best represents this situation?)
A: $40 $8 $99

Q: Consider the following situation: Bobby is at a county fair and is participating in "The Height Game". To play, the booth owner attempts to guess a participant's height. If the owner's guess is no more than 1 inch from the actual height, the owner wins the participant’s money. Otherwise, the participant wins a prize.

If Bobby's height is 75 inches, what inequality would give the range of values that the owner could guess in order to for Bobby to win a prize?
A: (a choice with no text)
If right: Correct. The difference between the guess and the actual height (75) needs to be less than or equal to 1 for the owner to win, meaning that for the owner to lose the difference must be greater than 1. Since the guess could be greater than or less than 75, use the absolute value symbol around the difference.
If wrong: Incorrect. Remember that the absolute value of the difference between the guess and the height (75) needs to be more than 1. Translate that into a mathematical inequality/sentence.
If wrong: Incorrect. Remember that the absolute value of the difference between the guess and the height (75) needs to be more than 1. Translate that into a mathematical inequality/sentence.
If wrong: Incorrect. Remember that the absolute value of the difference between the guess and the height (75) needs to be more than 1. Translate that into a mathematical inequality/sentence.

Q: Consider the following situation: Bobby is at a county fair and is participating in "The Height Game". To play, the booth owner attempts to guess a participant's height. If the owner's guess is no more than 0.5 inches from the actual height, the owner wins the participant's money. Otherwise, the participant wins a prize.

If Bobby's height is 75 inches, what inequality represents the range of values that the owner could guess in order for the owner to win?
- or (Incorrect. Choose values that the owner can guess and still win. Can he guess exactly .5 inches away?)
A: (a choice with no text)
If right: Correct. The difference between the guess and the actual height (75) needs to be less than or equal to 0.5 for the owner to win. The biggest guess the owner can make is 75.5 and still win, and the smallest guess the owner can make is 74.5 and still win. Any number between these two also allow for the owner to win.
If wrong: Incorrect. Choose values that the owner can guess and still win. Can he guess exactly .5 inches away?
If wrong: Incorrect. Choose values that the owner can guess and still win. Can he guess exactly .5 inches away?

Q: Brian and Hayden go out for dinner and the bill comes to $120.00. Hayden usually tips more than 20% of the bill and Brian usually tips at most 25% of the bill.

Given Brian and Hayden's tipping habits, what graph below best represents the range for a tip that the server should expect to see?
- $24 $30 (Correct. Hayden tips more than 20%, meaning that the server should expect more than $24 as a tip, but Brian tips at most 25% of the bill, meaning that the server should expect less than or equal to $30.)
- $24 $30 (Incorrect. Make sure the signs are correct; could the server get exactly 20% or 25%?)
- $24 $30 (Incorrect. Make sure the signs are correct; could the server get exactly 20% or 25%?)
- $24 (Incorrect. Make sure the signs are correct; could the server get exactly 20% or 25%?)
A: $24 $30

Q: Select the inequality that represents the following example.
A: (a choice with no text)
If wrong: Incorrect. Check to make sure your answer has the correct line (solid or dotted), the correct orientation (vertical or horizontal), and the correct shading (above vs. below, left vs. right). Which values of does this graph represent?
If wrong: Incorrect. Check to make sure your answer has the correct line (solid or dotted), the correct orientation (vertical or horizontal), and the correct shading (above vs. below, left vs. right). Which values of does this graph represent?
If right: Correct. The line is dotted, implying either a > or a < sign. The line is vertical, so it's a single-variable inequality with .
If wrong: Incorrect. Check to make sure your answer has the correct line (solid or dotted), the correct orientation (vertical or horizontal), and the correct shading (above vs. below, left vs. right). Which values of does this graph represent?

Q: Which graph represents the inequality 6"> ?
A: (a choice with no text)
If right: Correct. Solve the inequality for to get -2/3x+2"> . Graph the equation with a dotted line, and then shade above the line.
If wrong: Incorrect. First solve the inequality for to identify the boundary line. For which values of and will this inequality be true? Which region should be shaded?
If wrong: Incorrect. First solve the inequality for to identify the boundary line. For which values of and will this inequality be true? Which region should be shaded?
If wrong: Incorrect. First solve the inequality for to identify the boundary line. For which values of and will this inequality be true? Which region should be shaded?

Q: Which of the following points is a solution to the inequality ?
- (0, 1) (Incorrect. Check to make sure that your solution, when plugged into the and variables in the inequality, yields a true statement.)
- (-3, 2) (Incorrect. Check to make sure that your solution, when plugged into the and variables in the inequality, yields a true statement.)
- (3, 4) (Incorrect. Check to make sure that your solution, when plugged into the and variables in the inequality, yields a true statement.)
- (1, 0) (Correct. Plugging in (1, 0) for in the inequality yields a true statement.)
A: (1, 0)

Q: The point (-2, -2) is a solution to which one of the following inequalities?
A: (a choice with no text)
If wrong: Incorrect. Check to make sure that when plugging in (-2, -2) for , the inequality is true.
If wrong: Incorrect. Check to make sure that when plugging in (-2, -2) for , the inequality is true.
If right: Correct. Plugging in the values (-2, -2) for in the inequality yields a true statement.
If wrong: Incorrect. Check to make sure that when plugging in (-2, -2) for , the inequality is true.

Q: Which set of points below are all solutions to the inequality ?
- (2, 2), (3, 5), (-3, -5) (Incorrect. Points that are solutions to the inequality will have a coordinate that is less than or equal to the coordinate. Check to make sure that you've included only coordinates where the coordinate is less than or equal to the coordinate.)
- (1, 2), (3, 8), (-1, 0) (Incorrect. Points that are solutions to the inequality will have a coordinate that is less than or equal to the coordinate. Check to make sure that you've included only coordinates where the coordinate is less than or equal to the coordinate.)
- (9, 9), (2.5, 1), (-5, 0) (Incorrect. Points that are solutions to the inequality will have a coordinate that is less than or equal to the coordinate. Check to make sure that you've included only coordinates where the coordinate is less than or equal to the coordinate.)
- (9, -9), (2.75, 2.5), (-5, -5) (Correct. All three points in this set have a coordinate that is less than or equal to the coordinate.)
A: (9, -9), (2.75, 2.5), (-5, -5)