D. Correct! You translated the phrase exactly using x to represent the given real number.

Transcription

1 Problem Solving Drill 14: Solving and Graphing Linear Inequalities Question No. 1 of 10 Question 1. Which inequality represents the statement three more than seven times a real number is greater than or equal to five times the same real number? Question #01 (A) 7x + 3 5x (B) 7(x + 3) 5x (C) 3x + 7 5x (D) 7x + 3 5x You used the inequality sign in wrong direction. You added 3 to x before multiplying by x. You interchanged the roles of 3 and 7. D. Correct! You translated the phrase exactly using x to represent the given real number. The given real numbers = x 7x + 3 5x

2 Question No. 2 of 10 Question 2. Which number is a solution to 4x 8 > x? Question #02 (A) -3 (B) 2 (C) (D) 1 A. Correct! Solved the inequality by adding 8 and subtracting 4x from both sides. In final answer, you forgot the negative sign. When solving, you considered the boundary as one of the solutions. When comparing 1 with the solutions, you forgot the negative signs of the solutions. Subtract 4x and 11 from each side, and simplify; 4x x > x 4x > 8x Divide each side by 8. x < -19/8

3 Question No. 3 of 10 Question 3. What is the solution set of x 2 > 5? Question #03 (A) -3 < x < 7 (B) x < -3 or x > 7 (C) x > 7 (D) x > 3 B. Correct! The solution set to this inequality is x < -3 or x > 7. x 2 > 5 x 2 > 5 or x 2 < -5 Rewrite as two inequalities Isolate the variable in each part to solve. x > 7 x < -3

4 Question No. 4 of 10 Question 4. Which inequality is a true statement when x = -4? Question #04 (A) 3x 33 > 23x + 33 (B) x + 33 < 39 + x (C) 57 + x > 48 2x (D) 11(x + 4) > 8 x A. Correct! Replacing x = -4 in the inequality results in a true statement. Replace x = -4 into each inequality to find the answer choice that returns a true statement. Replace x = -4 into each inequality to find the answer choice that returns a true statement. Replace x = -4 into each inequality to find the answer choice that returns a true statement. Replace x = -4 in the inequality and check the result: 3(-4) 33 > 23(-4) > > -66 The outcome is true, so, x = -4 is a solution.

5 Question No. 5 of 10 Question 5. What is the solution set to the inequality 11(x 9) > 3x + 5? Question #05 (A) x > 1.75 (B) x < -52 (C) x > 13 (D) x < -13 Review how to solve multi-step inequalities and try again. Review how to solve multi-step inequalities and try again. C. Correct! You correctly distributed 11 over the parentheses and simplified the inequality. Review how to solve multi-step inequalities and try again. First, distribute 11 over the parentheses: 11(x 9) > 3x x 99 > 3x + 5 Add 99 to and subtract 3x from both sides and simplify. 11x x > 3x x 8x > 104 x > 13

6 Question No. 6 of 10 Question 6. Which inequality is represented by the graph? Question #06 (A) x < -3 and x > 2 (B) x 2 or x -3 (C) x 2 or x < -3 (D) x 2 and x -3 Review the rules for open and closed boundary points and compound inequalities. Review the rules for open and closed boundary points and compound inequalities. C. Correct! This inequality is an or compound inequality so it is shaded outside of the boundary points. Review the rules for open and closed boundary points and compound inequalities. The right highlighted portion of the graph indicated that the answer is x 2 or the left portion indicates that the answer is x < -3.

7 Question No. 7 of 10 Question 7. Which is the solution to the inequality 3m 2(m + 1) > 9m 34? Question #07 (A) m < 35 8 (B) m < 4.5 (C) m < 9 (D) m < 4 Review the steps for solving a multi-step inequality and try again. Review the steps for solving a multi-step inequality and try again. Review the steps for solving a multi-step inequality and try again. D. Correct! You removed the parentheses, combined like terms, and used inverse operations to find m < 4. Distribute the -2 over the parentheses, and simplify. 3m 2m - 2 > 9m 34 m 2 > 9m 34 m > 9m m 32 > 8m m < 4

8 Question No. 8 of 10 Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on 12paper as needed (3) Question 8. Which is the solution to 11 3x 22 22? Question #08 (A) 11 x 44 3 (B) -3 x 0 (C) 33 x 44 (D) 11 x 44 3 A. Correct! You added 22 to each part and simplified to get 11 x 44/3. Review the steps for solving a compound inequality and try again. Review the steps for solving a compound inequality and try again. Review the steps for solving a compound inequality and try again. Add 22 to each part, and simplify x x x 44/3

9 Question No. 9 of 10 Question 9. Which is the solution set of 9x 29 > 34? (A) 5 9 < x < 7 Question #09 (B) x > 7 or x < 65 9 (C) x > 7 or x < (D) x > 7 and x < This is not a disjunction inequality. Please try again. Check your arithmetic and try again. C. Correct! You wrote the two inequalities and solved both to get the answer. Check your arithmetic and try again. We have 9x 29 = 34 or -(9x 29) = 34 Solve the first equation. 9x = x = 63 x = 7 Solve the second equation. -9x + 29 = 34-9x = x = 5 x = -5/9

10 Question No. 10 of 10 Question 10. What is the solution to 5 3x 19 3 < 22? Question #10 (A) 4 < x < 8 (B) -1 < x < (C) 3 < x < 19 3 (D) 14 3 < x < 8 D. Correct! You isolated the absolute value on the left and then wrote the inequality as a compound inequality. Add 3 to each side and simplify 5 3x < x 19 < 25 Divide each side by 5 3x 19 < 5 Then -5 < 3x 19 < 5 Add 19 to all parts and simplify < 3x < < 3x < 8