Title: Unit 10 Quiz
Course: Technical Math for Industry

Q: Solve .
A: (a choice with no text)
If wrong: Incorrect. You may have thought that subtracting 17 from both sides of the equation would isolate the variable. However, if you do this you will get .
If wrong: Incorrect. To correctly use the addition property of equality you must add the same number to both sides of the equation. In this problem, you must add 17 to both sides. Be careful with the signs.
If wrong: Incorrect. You may have subtracted 23 from both sides of the equation. This will give you an equivalent equation, . However, this does not mean that x is equal to .
If right: Correct. Add 17 to both sides of the equation: , so .

Q: Solve for x:
A: (a choice with no text)
If wrong: Incorrect. You may have tried to apply the Addition Property of Equality by adding , instead of multiplying both sides of the equation by . Adding to will not leave you with x, and you must do the same thing to both sides.
If right: Correct. Multiply both sides of the equation by the multiplicative inverse of , which is : . Simplifying, or .
If wrong: Incorrect. It seems that you multiplied both sides by 2. This will lead you to , which is an equivalent equation, but it does not mean that x is equal to 12.
If wrong: Incorrect. It seems that you divided by instead of multiplying both sides of the equation by . Dividing by will not leave you with x, and you must do the same thing to both sides.

Q: Solve for x:
A: (a choice with no text)
If wrong: Incorrect. While trying to get the variable terms together on the left side, you may have added x to . To combine the variable terms, you would need to subtract x from both sides.
If wrong: Incorrect. While trying to get the constant terms together on the right side, you may have added 7 to 13. To combine the constant terms, you would need to subtract 7 from both sides.
If wrong: Incorrect. You may have made two mistakes. While trying to get the constant terms together on the right side, you may have added 7 to 13. To combine the constant terms, you would need to subtract 7 from both sides. While trying to get the variable terms together on the left side, you may have added x to . To combine the variable terms, you would need to subtract x from both sides.
If right: Correct. Subtract 7 from both sides: Subtract x from both sides: Divide both sides by 3:

Q: Solve:
A: (a choice with no text)
If wrong: Incorrect. You may have correctly used the distributive property to simplify the equation to , but then tried to subtract 8 to combine the constant terms. You need to add 8 to both sides to combine these terms.
If wrong: Incorrect. You may have correctly chosen to multiply both sides by 4 to clear the fractions, but forgot to multiply the constant terms, and 6, by 4. Make sure that you use the distributive property when you multiply each side of an equation by a number.
If wrong: Incorrect. You may have correctly used the distributive property to simplify the equation to , but then tried to subtract y to combine the variable terms. You need to add y to both sides to combine these terms.
If right: Correct. Multiply both sides by 4 to clear the fractions: Add 8 to both sides: Add y to both sides: Divide both sides by 4:

Q: Which of the following equations has the solution all real numbers?
A: (a choice with no text)
If wrong: Incorrect. Use the distributive property first, and then combine like terms on both sides. The equation will simplify to . Subtract from both sides to get . This is false, and it means that this equation has no solution.
If wrong: Incorrect. While simplifying, you may have made a mistake with signs. Use the distributive property first, and then combine like terms on both sides. The equation will simplify to . This equation has the solution .
If right: Correct. Use the distributive property on the left side to simplify: Combine like terms on both sides: Subtract from both sides: This means that the solution is all real numbers.
If wrong: Incorrect. You may have forgotten to distribute the 4 to the on the left side of the equation. The correct simplification is . This will simplify further to . This equation has the solution .

Q: Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $52, and then they charge her $8 per hour. She has $144 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.)
- 11.5 hours (Incorrect. You may have come up with the correct equation, , and solved it correctly, but Esmeralda cannot rent the car for a fraction of an hour. You need to interpret the answer in real-world terms.)
- 18 hours (Incorrect. You probably forgot to take into account the initial fee of $52, and divided the $144 by $8. If the number of hours, then Esmeralda is charged dollars plus the $52. So .)
- 12 hours (Incorrect. You may have come up with the correct equation, , and solved it correctly, but you misinterpreted the answer. Remember that Esmeralda can spend at most $144. She cannot spend more than this.)
- 11 hours (Correct. If the number of hours, then she is charged dollars plus the $52. So . Subtract 52 from both sides: . Divide both sides by 8: . She cannot rent the car for a fraction of an hour, so she can rent it for at most 11 hours.)
A: 11 hours

Q: Find the height of a triangle with an area (A) of 35 square inches and base (b) of 7 inches. Use the formula for the area of a triangle, .
- 10 inches (Correct. Substitute 35 for A and 7 for b: Multiply both sides by 2: Divide both sides by 7:)
- 122.5 inches (Incorrect. You may have incorrectly substituted 35 in place of h and found the resulting value of A. The correct substitution is:)
- 2.5 inches (Incorrect. You may have substituted and simplified correctly to get , but then divided by 2 instead of correctly multiplying both sides by 2.)
- 490 inches (Incorrect. You may have substituted and simplified correctly to get , but then multiplied by 7 instead of correctly dividing both sides by 7.)
A: 10 inches

Q: Solve the formula for the variable Q.
A: (a choice with no text)
If right: Correct. Subtract from both sides: Divide both sides by 3: Simplify to:
If wrong: Incorrect. It appears that you correctly subtracted from both sides. However, to isolate Q you then need to divide both sides by 3, not multiply.
If wrong: Incorrect. It seems that you made a mistake in your first step, trying to isolate the term . You cannot do this by adding . You need to subtract from both sides.
If wrong: Incorrect. This formula has been correctly solved for P, but the question asked for the original formula to be solved for Q.

Q: Which graph shows the inequality ?
A: (a choice with no text)
If wrong: Incorrect. Since 0 is not included in the solution, there should be an open circle at the end point 0. Also, since the values of x are greater than 0, the points on the graph should be to the right of 0.
If wrong: Incorrect. The values of x are greater than 0, so the points on the graph are to the right of 0. However, since 0 is not included in the solution, there should be an open circle at the end point 0.
If wrong: Incorrect. Since 0 is not included in the solution, there is an open circle at the end point 0. However, the values of x are greater than 0, so the points on the graph should be to the right of 0.
If right: Correct. Since 0 is not included in the solution, there is an open circle at the end point 0. The values of x are greater than 0, so the points on the graph are to the right of 0.

Q: Solve for c:
A: (a choice with no text)
If right: Correct. Add 7 to both sides: , so .
If wrong: Incorrect. You added incorrectly when trying to isolate the variable. You need to add 7 to both sides of the inequality. You may need to review the rules for adding negative and positive numbers.
If wrong: Incorrect. You may have correctly chosen to add 7 to both sides, but then made a mistake with the addition of a negative and positive number. Remember that the sign of the result is the sign of the number with the greater absolute value.
If wrong: Incorrect. You may have thought that you should subtract 7 from both sides of the inequality. However, you need to add 7 to both sides to isolate the variable.

Q: Solve for :
A: (a choice with no text)
If wrong: Incorrect. You may not have noticed that this is an equation, not an inequality. The solution to the given inequality is not one number, but an infinite set of numbers, which can be represented by an inequality.
If wrong: Incorrect. You may have thought that you needed to change the direction of the inequality sign because of the number . The first step to solving this inequality is to divide both sides by 7. Since you are dividing by a positive number, the inequality sign stays the same.
If wrong: Incorrect. You may have divided incorrectly when isolating the variable. Dividing a negative number by a positive number gives a negative quotient.
If right: Correct. Divide both sides by 7: , so .

Q: Solve for a.
A: (a choice with no text)
If wrong: Incorrect. You forgot to reverse the inequality sign when dividing both sides by to isolate the variable.
If wrong: Incorrect. You mistakenly tried to add 33 to both sides while isolating the variable term. Instead, you need to subtract 33 from both sides.
If wrong: Incorrect. You may have made a mistake when you divided both sides by to isolate the variable. Remember that a negative divided by a negative is positive.
If right: Correct. Subtract 33 from both sides: or Divide both sides by : or

Q: Solve for h.
A: (a choice with no text)
If wrong: Incorrect. You incorrectly tried to add 3 to both sides of the inequality to clear the parentheses. Adding 3 to the left side will not give you . You must use the distributive property on the left side to clear the parentheses.
If wrong: Incorrect. You forgot to reverse the inequality sign when dividing both sides by a negative number to isolate the variable.
If right: Correct. Use the distributive property on the left side: Subtract 3 from both sides: Add to both sides: Divide both sides by :
If wrong: Incorrect. While using the distributive property to clear the parentheses, you forgot that a negative number times a negative number is positive. So becomes , not .

Q: Which graph represents the solution to or ?
A: (a choice with no text)
If wrong: Incorrect. You may have chosen this graph because you are unclear on what the word or means in a compound inequality. It means that x can take on any values that make either one of the inequalities true. So the solution set will be all the points from the first inequality, plus all the points from the second inequality.
If wrong: Incorrect. This graph represents the solution to or . You may have chosen it because you thought a compound inequality with or had to show arrows in two directions, and you ignored the direction of the symbols in the solution.
If wrong: Incorrect. This graph shows the solution to or . You may have chosen it because you tried to subtract 9 from both sides of the second inequality, instead of adding 9 to both sides.
If right: Correct. To solve the first inequality, divide both sides by 7 to get . To solve the second inequality, add 9 to both sides and then divide by 6 to get . This means that the solution is all values of x greater than 3 or less than 5. Therefore, x could be any number, so the correct graph will include all real numbers.

Q: Which graph represents the solution to and ?
A: (a choice with no text)
If wrong: Incorrect. This graph represents the solution to . You may not have noticed that the solution should include the value 7 and would be graphed as a closed circle at that point.
If right: Correct. Solve the first inequality by subtracting 4 from both sides to get . Solve the second by adding 20 to both sides and then dividing by 8 to get . The solution of the compound inequality is the overlap of the two individual solutions. The graph of the solution falls between and 7, not including but including 7.
If wrong: Incorrect. This graph represents the solution to or . You may have incorrectly added 4 to both sides of the first inequality and incorrectly subtracted 20 from both sides of the second inequality while trying to isolate each variable.
If wrong: Incorrect. This graph is the solution to . You may not have noticed that the solution should not include the value and would be graphed as an open circle at that point.

Q: Solve for k.
A: (a choice with no text)
If right: Correct. Subtract 4 from all parts: Simplify to: Divide all parts by , and reverse the inequality signs. , so or
If wrong: Incorrect. You tried to add 4 to all parts of the inequality to isolate . Instead, you need to subtract 4 from all parts as your first step.
If wrong: Incorrect. You may have first added 6 to all parts of the inequality and thought that this eliminated the left side of the inequality. You cannot ignore or remove one part of the inequality, even if it has a 0. Instead, you should subtract 4 from all parts of the inequality in order to isolate .
If wrong: Incorrect. You forgot to reverse the inequality signs when you divided all parts of the inequality by . Also, this answer makes no sense, because it says that is at least 5, but at most 1.

Q: For which of the following compound inequalities is there no solution?
- and (Incorrect. The solution to this compound inequality is and . Their graphs intersect for , so the simplest description of the solution is any value greater than or equal to 4.)
- and (Correct. Divide both sides of the first inequality to get . Subtract 24 from both sides of the second inequality to get . Since the graphs of and have no overlap, there is no solution.)
- and (Incorrect. You may not have reversed the inequality sign in the first inequality when dividing both sides by . The two inequalities simplify to and . The solution to this compound inequality is all numbers greater than 8.)
- and (Incorrect. The solution to this compound inequality is and . Their graphs intersect for , so any value less than or equal to is a solution.)
A: and

Q: Solve for y:
- or (Correct. First subtract 8 from both sides of the equation, then rewrite as: or Add 3 to both sides of both equations: or Divide both sides of both equations by 6: or)
A: or
If wrong: Incorrect. You may have correctly subtracted 8 from both sides to get , but then solved . If , then or . In this problem, X is replaced by . So you should be solving and .
If wrong: Incorrect. You may have added 8 to as your first step, and then solved and . This means you are adding before finding absolute value, and that is not the correct order of operations. You need to subract 8 from both sides first, and then solve and .
If wrong: Incorrect. You may have correctly subtracted 8 from both sides to get , but then solved only . If , then or . In this problem, X is replaced by . So you should be solving two equations, and , but you forgot one of them.

Q: Solve the inequality:
- or (Incorrect. You may have mistakenly subtracted 6 from and then solved . This is an incorrect order of operations. Instead, you should simplify by adding 6 to both sides of the inequality to get . Then rewrite this without absolute value and solve the compound inequality.)
- or (Correct. Add 6 to both sides of the inequality: Rewrite without absolute value: or Subtract 2 from both sides of both inequalities: or Divide both sides of both inequalities by 6: or)
A: or
If wrong: Incorrect. You may have correctly simplified to , but then only found the solution to . When you rewrite the inequality without absolute value you should also get , which you must solve.
If wrong: Incorrect. You solved , instead of . You should first simplify to , and then rewrite without absolute value as or .

Q: Solve the equation:
- no solution (Correct. Subtract 1 from both sides of the equation: Divide both sides of the equation by : Since it's impossible to have an absolute value equal to a negative number, this equation has no solution.)
- or (Incorrect. You may have incorrectly simplified this to , and then solved or . Actually it simplifies to .)
- or (Incorrect. You may have correctly simplified this to , but then treated it as if it were , solving or . The correct way to simplify would be .)
- or (Incorrect. You probably thought that the equation simplified to , and then solved or . Actually it simplifies to .)
A: no solution