CLEP College Algebra - Problem Drill 21: Solving and Graphing Linear Inequalities No. 1 of 10 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? (A) 7x + 3 5x (B) 7(x + 3) 5x (C) 3x + 7 5x (D) 7x + 3 5x (E) 3x + 7 5x The wrong inequality sign is used. The number 3 was added to x before multiplying by x. The roles of 3 and 7 have been interchanged. D. Correct! You translated the phrase exactly using x to represent the given real number. The roles of 3 and 7 have been interchanged and the wrong inequality sign is used. Translate the verbal statement into numbers and math symbols. Three more than seven times a real number is greater than or equal to five times the same real number. +3 7x 5x 7x + 3 5x (D)7x + 3 5x
No. 2 of 10 2. Which number is a solution to 4x 8 > 11 + 12x? (A) -3 (B) -2 (C) 1 (D) 2 (E) 3 A. Correct! Substituting x = -3 into the inequality returns a true statement. Substituting x = -2 into the inequality returns a false statement. Substituting x = 1 into the inequality returns a false statement. Substituting x = 2 into the inequality returns a false statement. Substituting x = 3 into the inequality returns a false statement. Use inverse operations to isolate the variable. 4x 8 > 11 + 12x -8 > 11 + 8x -1 > 8x x < -1/8 The only answer choice in the solution set is x = -3. (A)-3
No. 3 of 10 3. What is the solution set of x 2 > 5? (A) -3 < x < 7 (B) x < -3 or x > 7 (C) x > 7 (D) x > 3 (E) x 7 B. Correct! The solution set to this inequality is x < -3 or x > 7. Write and solve the related disjunction inequality. x 2 > 5 x 2 > 5 or x 2 < -5 Rewrite as two inequalities. +2 +2 +2 +2 Isolate the variable in each part to solve. x > 7 x < -3 (B) x < -3 or x > 7
No. 4 of 10 4. Which inequality is a true statement when x = -4? (A) 3x 33 > 23x + 33 (B) x + 33 < 3 + x (C) 57 + x > 48 2x (D) 11(x + 4) > 8 x (E) 2x + 3 < -7 A. Correct! Substituting x = -4 in the inequality results in a true statement. Substitute x = -4 into each inequality to find the answer choice that returns a true statement. Substitute x = -4 into each inequality to find the answer choice that returns a true statement. Substitute x = -4 into each inequality to find the answer choice that returns a true statement. Substitute x = -4 into each inequality to find the answer choice that returns a true statement. Substitute x = -4 into each inequality to find the answer choice that returns a true statement. 3(-4) 33 > 23(-4) + 33-12 33 > -6 + 33-45 > -66 The outcome is true, so, x = -4 is a solution. (A) 3x - 33 > 23x + 33
No. 5 of 10 5. What is the solution set to the inequality 11(x ) > 3x + 5? (A) x < -52 (B) x < -13 (C) x < -1.5 (D) x > 1.75 (E) x > 13 E. Correct! You correctly distributed 11 over the parentheses and simplified the inequality. First, distribute 11 over the parentheses. 11(x ) > 3x + 5 11x > 3x + 5 Add to both sides. Then subtract 3x from both sides and simplify. 11x > 3x + 104 8x > 104 x > 13 (E) x > 13
No. 6 of 10 6. Which inequality is represented by the graph? (A) -3 < x < 2 (B) -3 < x 2 (C) -3 x 2 (D) x -3 or x 2 (E) x < -3 or x 2 The graphed solution set represents a disjunction inequality, not a conjunction. The graphed solution set represents a disjunction inequality, not a conjunction. The graphed solution set represents a disjunction inequality, not a conjunction. Review the rules for open and closed boundary points and compound inequalities. E. Correct! This inequality is an or compound inequality so it is shaded outside of the boundary points. The right highlighted portion of the graph indicated that the answer is x 2 and the left portion indicates that the answer is x < -3. This is a disjunction because the graph has two parts, so connect these inequalities with the word or. (E) x < -3 or x 2
No. 7 of 10 7. Which is the solution to the inequality 3m 2(m + 1) > m 34? (A) m < 4 (B) m < 4.375 (C) m < 4.5 (D) m < 4.7 (E) m < A. Correct! Remove the parentheses, combine like terms, and use inverse operations to find m < 4. Distribute the -2 over the parentheses and simplify. 3m 2m 2 > m 34 m 2 > m 34 m 2 + 34 > m 34 + 34 m 32 > 8m 4 > m m < 4 (A) m < 4
No. 8 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on 12paper as 8. What is the solution set for 11 3x 22 23? (A) 33 x 45 (B) 11 x 15 (C) -3 x 1 (D) -8 x 4 (E) -11 x 1 Review the steps for solving a compound inequality. B. Correct! You added 23 to each part and simplified to get 11 x 15. Review the steps for solving a compound inequality. Review the steps for solving a compound inequality. Review the steps for solving a compound inequality. Add 23 to each part then divide each part by 3 to reach the solution set. 11 + 23 3x 23 + 23 22 + 23 33 3x 45 11 x 15 (B) 11 x 15
No. of 10. What is the solution set of x 2 > 34? (A) (B) 43 x < or x > 7 65 x < or x > 7 5 (C) x < or x > 7 65 (D) < x < 7 (E) 5 < x < 7 Review the steps for finding the solution set of an absolute value inequality. Review the steps for finding the solution set of an absolute value inequality. C. Correct! You wrote the related disjunction inequality then simplified to get the solution set. Review the steps for finding the solution set of an absolute value inequality. Review the steps for finding the solution set of an absolute value inequality. Write the related disjunction inequality. x 2 > 34 or x 2 < -34 Solve the first inequality. x 2 > 34 x > 63 x > 7 Solve the second inequality. x 2 < -34 x < -5 5 x < The solution set is 5 x < or x > 7. (C) x < -(5/) or x > 7
No. 10 of 10 10. What is the solution set for 5 3x 1 3 < 22? (A) 4 < x < 8 (B) (C) 1 < x < 41 3 14 1 < x < 3 3 (D) 14 < x < 8 3 (E) 5 < 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 1 3 < 22 5 3x 1 < 25 Divide each side by 5. 3x 1 < 5 Write the related conjunction equality. -5 < 3x 1 < 5 Add 1 to all parts and simplify. -5 + 1 < 3x 1 + 1 < 5 + 1 14 3 < x < 8 (D) 14 < x < 8 3