A. Incorrect! This inequality is a disjunction and has a solution set shaded outside the boundary points.

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1 Problem Solving Drill 11: Absolute Value Inequalities Question No. 1 of 10 Question 1. Which inequality has the solution set shown in the graph? Question #01 (A) x + 6 > 1 (B) x + 6 < 1 (C) x (D) x This inequality is a disjunction and has a solution set shaded outside the boundary points. B. Correct! This inequality simplifies to the conjunction -7 < x < -5. This inequality is a disjunction and has a solution set shaded outside the boundary points. This disjunction has closed boundary points. This inequality is a conjunction with closed boundary points. x + 6 < 1-1 < x + 6 < < x < The solution set is shaded between the boundary points, so this is a conjunction. 2. Conjunctions use the symbols < or when the absolute value expression is to the left. 3. The boundary points are open so the boundary points are not included. Use the symbol <. 4. Solve this inequality by removing the absolute value brackets and inserting -7 < to the right of the expression. 5. Isolate the variable by subtracting 6 from all parts of the inequality.

2 Question No. 2 of 10 Question 2. Find the solution set to the inequality: 2x 1 5 Question #02 (A) x 3 (B) x -3 or x 3 (C) -2 x 2 (D) -3 x 3 You are missing the second boundary point. Remember to create the related conjunction inequality then solve. The solution should be a conjunction. Check to make sure your related inequality is a conjunction. Make sure you are using opposite operations to isolate the absolute value expression. D. Correct! Isolate the absolute value expression by adding 1 to both sides. Solve the related conjunction -6 x 6 to reach the solution set -3 x 3. 2x x 6 1. Isolate the absolute value expression by adding 1 to both sides. -6 2x 6 2. Create the related conjunction and solve x 3

3 Question No. 3 of 10 Question 3. Which value is in the solution set for 7 3x < -17? Question #03 (A) -9 (B) 8 (C) -3 (D) 1 A. Correct! Plugging -9 into the inequality results in a true statement. Plugging 8 into the inequality results in a false statement. Plugging -3 into the inequality results in a false statement. Plugging 1 into the inequality results in a false statement. 7 3x < Isolate the absolute value expression x < x > 24 3x > 24 or 3x < Create the related disjunction inequality and solve each part x > 8 or x < Find which answer choice returns a true statement.

4 Question No. 4 of 10 Question 4. Which inequality has the solution set shown in the graph? Question #04 (A) 2x 3 5 (B) 2x 3 5 (C) 2x 3 5 (D) 2x 3 5 This inequality is a conjunction and has a solution set shaded between the boundary points -4 and 4. This inequality simplifies to the solution set -1 x 4. C. Correct! This inequality simplifies to the solution set x -4 or x 4. This inequality simplifies to the solution set x -1 or x 4. 2x x 8 2x 8 or 2x x 4 or x The solution set is shaded outside the boundary points so this is a disjunction. 2. Solve the two disjunctions (C and D) to find the one with the solution set in the graph.

5 Question No. 5 of 10 Question 5. Find the solution set to the inequality: x + 7 > 4 Question #05 (A) -11 < x < -3 (B) x > -3 (C) x < -11 or x > -3 (D) x < -11 This solution set is a conjunction but the original inequality is a disjunction. Please try again. The solution set to the given inequality has two boundary points. C. Correct! The solution set to this inequality is x < -11 or x > -3. The solution set to the given inequality has two boundary points. x + 7 > 4 x + 7 > 4 or x + 7 < x > -3 x < Create the related disjunction. 2. Solve each part of the disjunction by isolating the variable using inverse operations. 3. The solution set is x < -11 or x > -3.

6 Question No. 6 of 10 Question 6. Which value is in the solution set for x 6 < 1? Question #06 (A) 7 (B) 3 (C) 10 (D) -8 Plugging 7 into the inequality results in a false statement. B. Correct! Plugging 3 into the inequality results in a true statement. Plugging 10 into the inequality results in a false statement. Plugging -8 into the inequality results in a false statement. x 6 < x < 7 1. Isolate the absolute value expression. -7 < x < 7 2. Create the related conjunction inequality and find which answer choice returns a true statement.

7 Question No. 7 of 10 Question 7. Which inequality has the solution set shown in the graph? Question #07 (A) 7 x + 9 > 21 (B) 7 x + 9 < 21 (C) 7 x (D) 7 x The graph of this inequality would have open boundary points at -12 and -6, and the solution set would be shaded outside the boundary points. The graph of this inequality would have open boundary points at -12 and -6. The solution set of this inequality would be shaded outside the boundary points. D. Correct! This inequality simplifies to the conjunction -12 x x x x x The solution set is shaded between the boundary points so this is a conjunction. 2. Solve the two conjunctions (B and D) to find the one with the solution set in the graph.

8 Question No. 8 of 10 Question 8. Find the solution set to the inequality 4 + x > 9. Question #08 (A) x < -13 or x > 5 (B) -13 < x < 5 (C) x > 5 (D) x > 13 A. Correct! The solution set to the inequality is x < -13 or x > 5. This solution set is a conjunction but the given inequality is a disjunction. The solution set of the given inequality will have two boundary points. The solution set of the given inequality will have two boundary points. 4 + x > x > 9 or 4 + x < x > 5 x < Write the two inequalities that make up this disjunction. 2. Solve both inequalities.

9 Question No. 9 of 10 Question 9. Which value is in the solution set for 5 x < 2? Question #09 (A) 7 (B) 3 (C) -5 (D) 6 Plugging 7 into the given inequality results in a false statement. Plugging 3 into the given inequality results in a false statement. Plugging -5 into the given inequality results in a false statement. D. Correct! Plugging 6 into the given inequality results in a true statement. 5 x < 2-2 < 5 x < 2 1. Create the related conjunction inequality and isolate x < -x < -3 7 > x > 3 3 < x < 7 2. Find which answer choice returns a true statement.

10 Question No. 10 of 10 Question 10. Which inequality has the solution set shown in the graph? Question #10 (A) x 4 2 (B) x 4 > 2 (C) x 4 2 (D) x 4 < 2 The graph of this inequality has closed boundary points at 2 and 6 and is shaded between the boundary points. B. Correct! This inequality has a solution set of x < 2 or x > 6. The graph of this inequality has closed boundary points. The graph of this inequality is shaded between the boundary points. x 4 > 2 x 4 > 2 or x 4 < x > 6 x < 2 1. The solution set is shaded outside the boundary points so this is a disjunction, so the sign used is either > or. 2. The boundary points are open so we know the sign used is >.