Key rules A number is rational if it can be written as p q \frac{p}{q} q p with integers p , q p, q p , q and q ≠ 0 q \neq 0 q = 0 . Terminating and repeating decimals are rational; non-terminating, non-repeating decimals (like 5 \sqrt{5} 5 , π \pi π ) are irrational. Multiplying or dividing an inequality by a negative number reverses the inequality sign. Interval notation: [ a , b ] [a,b] [ a , b ] includes endpoints, ( a , b ) (a,b) ( a , b ) excludes them, and ∞ \infty ∞ always gets a round bracket. ∣ x ∣ < a ⟺ − a < x < a |x| < a \iff -a < x < a ∣ x ∣ < a ⟺ − a < x < a , and ∣ x ∣ > a ⟺ x < − a |x| > a \iff x < -a ∣ x ∣ > a ⟺ x < − a or x > a x > a x > a (for a > 0 a > 0 a > 0 ). Also a 2 = ∣ a ∣ \sqrt{a^2} = |a| a 2 = ∣ a ∣ . For quadratic and rational inequalities, move everything to one side, find where the expression is zero or undefined, and use a sign table. Visual guide Number lines for the intervals (−1, 4], [2, ∞) and (−3, 3). Open circles mark endpoints that are not included, closed circles mark endpoints that are included. (−1, 4] −1 < x ≤ 4 −5 −4 −3 −2 −1 0 1 2 3 4 5 [2, ∞) x ≥ 2 −5 −4 −3 −2 −1 0 1 2 3 4 5 (−3, 3) |x| < 3 −5 −4 −3 −2 −1 0 1 2 3 4 5 Interval notation on a number line. An open circle means the endpoint is not included, a closed circle means it is. Infinity always gets a round bracket.
Questions 84 total 1 Book example Example 1 Classify each of the following numbers as rational or irrational: { 3 5 , − 7 , 0.125 , 0.666 … , 5 , π } \left\{\frac{3}{5}, -7, 0.125, 0.666\ldots, \sqrt{5}, \pi\right\} { 5 3 , − 7 , 0.125 , 0.666 … , 5 , π } 2 Related problem Related Problem 1 Classify each of the following numbers as rational or irrational: { 7 9 , 7 , 0.2 , 2 ⋅ 8 , − 0.75 , 2 5 , π − 3 } \left\{\frac{7}{9}, \sqrt{7}, 0.2, \sqrt{2}\cdot\sqrt{8}, -0.75, 2\sqrt{5}, \pi - 3\right\} { 9 7 , 7 , 0.2 , 2 ⋅ 8 , − 0.75 , 2 5 , π − 3 } 3 Related problem Required Related Problem 2a Solve the linear inequality and write the answer in interval notation: 3 x + 4 > 16 3x + 4 > 16 3 x + 4 > 16 4 Related problem Required Related Problem 2b Solve the linear inequality and write the answer in interval notation: 5 − 2 x < 9 5 - 2x < 9 5 − 2 x < 9 5 Related problem Related Problem 2c Solve the linear inequality and write the answer in interval notation: 5 − 3 ( 2 x + 1 ) < 4 x − 7 5 - 3(2x + 1) < 4x - 7 5 − 3 ( 2 x + 1 ) < 4 x − 7 6 Related problem Required Related Problem 2d Solve the linear inequality and write the answer in interval notation: 2 x − 1 3 ≤ x − 4 \frac{2x - 1}{3} \le x - 4 3 2 x − 1 ≤ x − 4 7 Book example Example 5 Solve the inequality ∣ 3 x + 1 ∣ > 7 |3x + 1| > 7 ∣3 x + 1∣ > 7 . 8 Book example Example 6 Solve the inequality ( x − 3 ) 2 < 5 \sqrt{(x - 3)^2} < 5 ( x − 3 ) 2 < 5 . 9 Related problem Related Problem 3a Solve the inequality: ∣ x − 3 ∣ ≤ 4 |x - 3| \le 4 ∣ x − 3∣ ≤ 4 10 Related problem Related Problem 3b Solve the inequality: ∣ 2 x + 1 ∣ > 0 |2x + 1| > 0 ∣2 x + 1∣ > 0 11 Related problem Related Problem 3c Solve the inequality: ∣ x + 2 ∣ < − 1 |x + 2| < -1 ∣ x + 2∣ < − 1 12 Related problem Related Problem 3d Solve the inequality: ∣ 3 x − 4 ∣ ≥ − 2 |3x - 4| \ge -2 ∣3 x − 4∣ ≥ − 2 13 Book example Example 8 Solve the inequality x 2 + 4 x < 5 x^2 + 4x < 5 x 2 + 4 x < 5 . 14 Book example Example 9 Solve the inequality x 2 − 4 x + 4 < 0 x^2 - 4x + 4 < 0 x 2 − 4 x + 4 < 0 . 15 Book example Example 10 Solve the inequality x 2 + 2 x + 5 > 0 x^2 + 2x + 5 > 0 x 2 + 2 x + 5 > 0 . 16 Related problem Required Related Problem 5a Solve the inequality: x − 1 x + 2 ≥ 0 \frac{x - 1}{x + 2} \ge 0 x + 2 x − 1 ≥ 0 17 Related problem Required Related Problem 5b Solve the inequality: x 2 − 9 x − 3 > 0 \frac{x^2 - 9}{x - 3} > 0 x − 3 x 2 − 9 > 0 18 Related problem Required Related Problem 5c Solve the inequality: 2 x − 3 ≥ 1 x + 1 \frac{2}{x - 3} \ge \frac{1}{x + 1} x − 3 2 ≥ x + 1 1 19 Related problem Related Problem 5d Solve the inequality: ( x − 2 ) ( x + 1 ) ( x − 3 ) 2 ≤ 0 \frac{(x - 2)(x + 1)}{(x - 3)^2} \le 0 ( x − 3 ) 2 ( x − 2 ) ( x + 1 ) ≤ 0 20 Book exercise Required Exercises 1.1, #1 Solve the inequality: 3 x − 5 ≤ 7 3x - 5 \le 7 3 x − 5 ≤ 7 21 Book exercise Required Exercises 1.1, #3 Solve the inequality: 5 − 3 x ≤ − 4 5 - 3x \le -4 5 − 3 x ≤ − 4 22 Book exercise Required Exercises 1.1, #7 Solve the inequality: 2 ( x − 1 ) ≤ 2 x + 3 2(x - 1) \le 2x + 3 2 ( x − 1 ) ≤ 2 x + 3 23 Book exercise Required Exercises 1.1, #9 Solve the inequality: ∣ x − 3 ∣ ≤ 5 |x - 3| \le 5 ∣ x − 3∣ ≤ 5 24 Book exercise Required Exercises 1.1, #10 Solve the inequality: ∣ 2 x + 1 ∣ > 7 |2x + 1| > 7 ∣2 x + 1∣ > 7 25 Book exercise Required Exercises 1.1, #13 Solve the inequality: ∣ x − 1 ∣ < 0 |x - 1| < 0 ∣ x − 1∣ < 0 26 Book exercise Required Exercises 1.1, #16 Solve the inequality: ( x + 1 ) 2 < 4 \sqrt{(x + 1)^2} < 4 ( x + 1 ) 2 < 4 27 Book exercise Required Exercises 1.1, #19 Solve the inequality: x 2 + 4 ≤ 4 x x^2 + 4 \le 4x x 2 + 4 ≤ 4 x 28 Book exercise Required Exercises 1.1, #23 Solve the inequality: 2 x 2 − 3 x < 2 2x^2 - 3x < 2 2 x 2 − 3 x < 2 29 Book exercise Required Exercises 1.1, #25 Solve the inequality: x + 3 x − 1 < 0 \frac{x + 3}{x - 1} < 0 x − 1 x + 3 < 0 30 Book exercise Required Exercises 1.1, #27 Solve the inequality: 1 x − 2 > 3 x + 1 \frac{1}{x - 2} > \frac{3}{x + 1} x − 2 1 > x + 1 3 31 Self test MCQ Required Self Learning Test #1 Solve the inequality 3 x − 7 ≤ 5 3x - 7 \le 5 3 x − 7 ≤ 5 . 32 Self test MCQ Required Self Learning Test #2 Solve the inequality ∣ x − 2 ∣ < 3 |x - 2| < 3 ∣ x − 2∣ < 3 . 33 Self test MCQ Required Self Learning Test #3 Solve the inequality x 2 − 4 ≥ 0 x^2 - 4 \ge 0 x 2 − 4 ≥ 0 . 34 Self test MCQ Self Learning Test #4 Solve the inequality x − 1 ≥ 0 \sqrt{x - 1} \ge 0 x − 1 ≥ 0 . 35 Self test MCQ Required Self Learning Test #5 Solve the inequality ∣ 2 x + 1 ∣ ≥ 5 |2x + 1| \ge 5 ∣2 x + 1∣ ≥ 5 . 36 Self test MCQ Required Self Learning Test #6 Solve the inequality x 2 − 5 x + 6 < 0 x^2 - 5x + 6 < 0 x 2 − 5 x + 6 < 0 . 37 Self test MCQ Required Self Learning Test #7 Solve the inequality x − 1 x + 2 > 0 \frac{x - 1}{x + 2} > 0 x + 2 x − 1 > 0 . 38 Self test MCQ Required Self Learning Test #8 Solve the inequality ∣ x 2 − 1 ∣ ≤ 2 ∣ x − 1 ∣ |x^2 - 1| \le 2|x - 1| ∣ x 2 − 1∣ ≤ 2∣ x − 1∣ . 39 Self test MCQ Required Self Learning Test #9 Solve the inequality x 2 − 4 x − 2 ≤ 0 \frac{x^2 - 4}{x - 2} \le 0 x − 2 x 2 − 4 ≤ 0 . 40 Self test MCQ Required Self Learning Test #10 Solve the inequality ∣ x − 1 x + 1 ∣ ≥ 1 \left|\frac{x - 1}{x + 1}\right| \ge 1 x + 1 x − 1 ≥ 1 . 41 Book exercise Required Challenging Problems #4 Solve the inequality: x 2 − 4 x + 5 < ∣ x − 1 ∣ \sqrt{x^2 - 4x + 5} < |x - 1| x 2 − 4 x + 5 < ∣ x − 1∣ 42 Book exercise Required Applications #4 An air-conditioning system in a mosque must keep the temperature within 3 ∘ C 3^\circ C 3 ∘ C of 22 ∘ C 22^\circ C 2 2 ∘ C during prayer times. Write an inequality for the acceptable temperature range and express the solution in interval notation. 43 Tutorial Tutorial 1+2, Q1 A Classify each of the following numbers as rational or irrational: { π cos π , − 125 3 5 , 22 7 , 2.476476 … , ( 2 + 18 ) 2 , ( 3 + 12 ) 3 , ( 2 ) 7 , ( 2 3 + 3 2 ) } \left\{\pi\cos\pi, \frac{\sqrt[3]{-125}}{\sqrt{5}}, \frac{22}{7}, 2.476476\ldots, (\sqrt{2} + \sqrt{18})^2, (\sqrt{3} + \sqrt{12})^3, (\sqrt{2})^7, \left(\frac{\sqrt{2}}{\sqrt{3}} + \frac{\sqrt{3}}{\sqrt{2}}\right)\right\} { π cos π , 5 3 − 125 , 7 22 , 2.476476 … , ( 2 + 18 ) 2 , ( 3 + 12 ) 3 , ( 2 ) 7 , ( 3 2 + 2 3 ) } 44 Tutorial Tutorial 1+2, Q1 B1 Solve the inequality and write the solution in interval notation: − 2 ≤ 3 x − 1 < 7 -2 \le 3x - 1 < 7 − 2 ≤ 3 x − 1 < 7 45 Tutorial Tutorial 1+2, Q1 B2 Solve the inequality and write the solution in interval notation: 2 x − 1 < 1 x + 3 \frac{2}{x - 1} < \frac{1}{x + 3} x − 1 2 < x + 3 1 46 Tutorial Tutorial 1+2, Q2 1 Solve the inequality and write the solution in interval notation: ( x + 1 ) 2 < 16 \sqrt{(x + 1)^2} < 16 ( x + 1 ) 2 < 16 47 Tutorial Tutorial 1+2, Q2 2 Solve the inequality and write the solution in interval notation: ∣ 3 x − 4 ∣ ≥ 2 |3x - 4| \ge 2 ∣3 x − 4∣ ≥ 2 48 Tutorial Tutorial 1+2, Q2 3 Solve the inequality and write the solution in interval notation: x 2 + 4 ≤ 4 x x^2 + 4 \le 4x x 2 + 4 ≤ 4 x 49 Past midterm Midterm 1446H S1, Q1 A Classify each of the following numbers into rational or irrational: { 3.14 , sin 2 ( π 5 ) + cos 2 ( π 5 ) , 32 5 , 2.34218 … , 2. 4 ‾ , 3 2 , tan ( π 4 ) , ( 2 + 18 ) 2 } \left\{3.14, \sin^2\left(\frac{\pi}{5}\right) + \cos^2\left(\frac{\pi}{5}\right), \sqrt[5]{32}, 2.34218\ldots, 2.\overline{4}, \frac{3}{\sqrt{2}}, \tan\left(\frac{\pi}{4}\right), \left(\sqrt{2} + \sqrt{18}\right)^2\right\} { 3.14 , sin 2 ( 5 π ) + cos 2 ( 5 π ) , 5 32 , 2.34218 … , 2. 4 , 2 3 , tan ( 4 π ) , ( 2 + 18 ) 2 } 50 Past midterm Midterm 1446H S1, Q1 B(i) Solve the inequality and write your answer in interval notation: 3 x − 7 4 < 9 x − 1 2 ≤ 3 x + 10 4 \frac{3x - 7}{4} < \frac{9x - 1}{2} \le \frac{3x + 10}{4} 4 3 x − 7 < 2 9 x − 1 ≤ 4 3 x + 10 51 Past midterm Midterm 1446H S1, Q1 B(ii) Solve the inequality and write your answer in interval notation: x 2 ≤ 2 x + 8 x^2 \le 2x + 8 x 2 ≤ 2 x + 8 52 Past midterm Alternative Midterm 1446H S1, Q1 A Classify each of the following numbers into rational or irrational: { 25 + 16 3 , sin ( 2 π 3 ) , cos ( 2 π 3 ) , 3. 5 ‾ , 5.149 … , 64 , ( 2 + 8 ) 2 , 22 7 } \left\{\sqrt[3]{\sqrt{25} + \sqrt{16}}, \sin\left(\frac{2\pi}{3}\right), \cos\left(\frac{2\pi}{3}\right), 3.\overline{5}, 5.149\ldots, \sqrt{64}, \left(\sqrt{2} + \sqrt{8}\right)^2, \frac{22}{7}\right\} { 3 25 + 16 , sin ( 3 2 π ) , cos ( 3 2 π ) , 3. 5 , 5.149 … , 64 , ( 2 + 8 ) 2 , 7 22 } 53 Past midterm Alternative Midterm 1446H S1, Q1 B(i) Solve the inequality and write your answer in interval notation: 2 x − 3 ≥ 1 x + 1 \frac{2}{x - 3} \ge \frac{1}{x + 1} x − 3 2 ≥ x + 1 1 54 Past midterm Alternative Midterm 1446H S1, Q1 B(ii) Solve the inequality and write your answer in interval notation: − 6 < 2 x − 4 5 ≤ 4 -6 < \frac{2x - 4}{5} \le 4 − 6 < 5 2 x − 4 ≤ 4 55 Past midterm Midterm 1446H (photo), Q1 A Classify each of the following numbers into rational or irrational: { 2 3 2 , 3 + 2. 4 ‾ , 3 7 , 2 , sin ( π 4 ) , ( 5 ) 4 , ( 2 ) 7 , 3.279 … } \left\{2\tfrac{3}{2}, 3 + 2.\overline{4}, 3\sqrt{7}, \sqrt{2}, \sin\left(\frac{\pi}{4}\right), \left(\sqrt{5}\right)^4, \left(\sqrt{2}\right)^7, 3.279\ldots\right\} { 2 2 3 , 3 + 2. 4 , 3 7 , 2 , sin ( 4 π ) , ( 5 ) 4 , ( 2 ) 7 , 3.279 … } 56 Past midterm Midterm 1446H (photo), Q1 B(i) Solve the inequality and write your answer in interval notation: 4 − 2 ( 2 − 3 x ) ≥ 2 ( 5 x − 5 ) 4 - 2(2 - 3x) \ge 2(5x - 5) 4 − 2 ( 2 − 3 x ) ≥ 2 ( 5 x − 5 ) 57 Past midterm Midterm 1446H (photo), Q1 B(ii) Solve the inequality and write your answer in interval notation: x 2 − 5 x 2 − x − 6 + 4 5 ( x + 2 ) ≥ 4 5 ( x − 3 ) \frac{x^2 - 5}{x^2 - x - 6} + \frac{4}{5(x + 2)} \ge \frac{4}{5(x - 3)} x 2 − x − 6 x 2 − 5 + 5 ( x + 2 ) 4 ≥ 5 ( x − 3 ) 4 58 Question bank Midterm 1443H S1, Q1 A Classify each of the following numbers into rational or irrational: { 2.4 , 3.14 , 27 125 , 25 + 16 3 , 7. 5 ‾ , sin ( π 6 ) , 1 3 , 2.45971 … } \left\{2.4, 3.14, \sqrt{\frac{27}{125}}, \sqrt[3]{\sqrt{25} + \sqrt{16}}, 7.\overline{5}, \sin\left(\frac{\pi}{6}\right), \frac{1}{3}, 2.45971\ldots\right\} { 2.4 , 3.14 , 125 27 , 3 25 + 16 , 7. 5 , sin ( 6 π ) , 3 1 , 2.45971 … } 59 Question bank Midterm 1443H S1, Q1 B Solve the inequality and write your answer in interval notation: 3 x − 11 ≤ 1 3x - 11 \le 1 3 x − 11 ≤ 1 60 Question bank Midterm 1442H S1, Q1 A Classify each of the following numbers into rational or irrational: { ( 1. 3 ‾ ) 2 , 3.14 6 , sin ( π 3 ) , 9 16 , π 2 , 22 7 , 8 3 , 2 } \left\{(1.\overline{3})^2, \frac{3.14}{6}, \sin\left(\frac{\pi}{3}\right), \sqrt{\frac{9}{16}}, \frac{\pi}{2}, \frac{22}{7}, \sqrt[3]{8}, \sqrt{2}\right\} { ( 1. 3 ) 2 , 6 3.14 , sin ( 3 π ) , 16 9 , 2 π , 7 22 , 3 8 , 2 } 61 Question bank Midterm 1442H S1, Q1 B(i) Solve the inequality and write your answer in interval notation: 3 x + 5 ≥ x + 1 3x + 5 \ge x + 1 3 x + 5 ≥ x + 1 62 Question bank Midterm 1442H S2, Q1 A(i) Solve the inequality and write your answer in interval notation: ∣ 3 x + 5 ∣ − ∣ 2 x − 5 ∣ < 0 |3x + 5| - |2x - 5| < 0 ∣3 x + 5∣ − ∣2 x − 5∣ < 0 63 Question bank Midterm 1442H S2, Q1 A(ii) Solve the inequality and write your answer in interval notation: 5 x + 4 ≥ 2 x − 5 5x + 4 \ge 2x - 5 5 x + 4 ≥ 2 x − 5 64 Question bank Midterm 1442H S2, Q1 B Classify each of the following numbers into rational or irrational: { 0.7 , sin π 3 , 4 + 5 , 1.1 , cos π 3 , 5 3 , ( 32 + 2 ) 2 , 3.14 } \left\{0.7, \sin\frac{\pi}{3}, \sqrt{4 + 5}, 1.1, \cos\frac{\pi}{3}, \sqrt{5^3}, \left(\sqrt{32} + \sqrt{2}\right)^2, 3.14\right\} { 0.7 , sin 3 π , 4 + 5 , 1.1 , cos 3 π , 5 3 , ( 32 + 2 ) 2 , 3.14 } 65 Question bank Alternative Midterm 1443H S1, Q1 (1) Solve the inequality and write your answer in interval notation: 4 x − 2 < 6 x + 5 4x - 2 < 6x + 5 4 x − 2 < 6 x + 5 66 Question bank Alternative Midterm 1443H S1, Q1 (2) Solve the inequality and write your answer in interval notation: ∣ 2 − 4 x ∣ ≥ 6 |2 - 4x| \ge 6 ∣2 − 4 x ∣ ≥ 6 67 Question bank Midterm 1443H S2, Q1 A Classify each of the following numbers into rational or irrational: { 0.123123 , 25 + π , sin ( π 3 ) , 9 + 1 , 3 3 , 7.8 3 ‾ , 3.14 , 0.345 … } \left\{0.123123, \sqrt{25} + \pi, \sin\left(\frac{\pi}{3}\right), \sqrt{\sqrt{9} + 1}, \frac{\sqrt{3}}{3}, 7.8\overline{3}, 3.14, 0.345\ldots\right\} { 0.123123 , 25 + π , sin ( 3 π ) , 9 + 1 , 3 3 , 7.8 3 , 3.14 , 0.345 … } 68 Question bank Midterm 1443H S2, Q1 B Solve the inequality and write your answer in interval notation: 3 ( x + 2 ) − 1 < 5 x 3(x + 2) - 1 < 5x 3 ( x + 2 ) − 1 < 5 x 69 Question bank Midterm 1438H S1, Q1 A Solve the inequality and write your answer in interval notation: − 5 < 2 x − 3 ≤ 7 -5 < 2x - 3 \le 7 − 5 < 2 x − 3 ≤ 7 70 Question bank Alternative Midterm 1438H S1, Q1 A Solve the inequality and write your answer in interval notation: 3 − 2 ∣ 3 x − 1 ∣ ≥ 6 3 - 2|3x - 1| \ge 6 3 − 2∣3 x − 1∣ ≥ 6 71 Question bank Alternative Midterm 1438H S2, Q1 B Solve the inequality and write your answer in interval notation: 1 − 2 ∣ 2 x − 3 ∣ ≥ − 6 1 - 2|2x - 3| \ge -6 1 − 2∣2 x − 3∣ ≥ − 6 72 Question bank First Midterm 1439/1440H S1, Q1 A Classify each of the following numbers into rational and irrational: { 2 , 7 9 , 2.7 6 ‾ , 3 π 2 } \left\{\sqrt{2}, \frac{7}{\sqrt{9}}, 2.7\overline{6}, \frac{3\pi}{2}\right\} { 2 , 9 7 , 2.7 6 , 2 3 π } 73 Question bank First Midterm 1439/1440H S1, Q1 B(1) Solve the inequality and write your answer in interval notation: 3 x + 5 ≤ − 10 3x + 5 \le -10 3 x + 5 ≤ − 10 74 Question bank First Midterm 1439/1440H S1, Q1 B(2) Solve the inequality and write your answer in interval notation: 0 < ∣ 2 x − 3 ∣ < 6 0 < |2x - 3| < 6 0 < ∣2 x − 3∣ < 6 75 Question bank First Midterm 1441H S1, Q1 A Classify each of the following numbers into rational or irrational: { 27 3 , 8 2 , 3 π , 25 + 16 , 7. 5 ‾ , 2 3 , 4.952 + 1 3 , 2.45971 … } \left\{\sqrt[3]{27}, \frac{\sqrt{8}}{\sqrt{2}}, 3\pi, \sqrt{\sqrt{25} + \sqrt{16}}, 7.\overline{5}, \sqrt[3]{2}, 4.952 + \frac{1}{3}, 2.45971\ldots\right\} { 3 27 , 2 8 , 3 π , 25 + 16 , 7. 5 , 3 2 , 4.952 + 3 1 , 2.45971 … } 76 Question bank First Midterm 1441H S1, Q1 B(i) Solve the inequality and write your answer in interval notation: 6 x − 2 ≥ x + 8 6x - 2 \ge x + 8 6 x − 2 ≥ x + 8 77 Question bank First Midterm 1441H S1, Q1 B(ii) Solve the inequality and write your answer in interval notation: 1 ∣ x − 1 ∣ < 1 ∣ x − 2 ∣ \frac{1}{|x - 1|} < \frac{1}{|x - 2|} ∣ x − 1∣ 1 < ∣ x − 2∣ 1 78 Question bank First Midterm 1439/1440H S2, Q1 A Classify each of the following numbers into rational and irrational: { 2. 34 ‾ , 8 3 , 2 5 , 3 2 } \left\{2.\overline{34}, \sqrt[3]{8}, \frac{2}{5}, \frac{3}{\sqrt{2}}\right\} { 2. 34 , 3 8 , 5 2 , 2 3 } 79 Question bank First Midterm 1439/1440H S2, Q1 B(1) Solve the inequality and write your answer in interval notation: 2 x − 1 ≤ 3 x + 4 2x - 1 \le 3x + 4 2 x − 1 ≤ 3 x + 4 80 Question bank First Midterm 1439/1440H S2, Q1 B(2) Solve the inequality and write your answer in interval notation: 4 − 2 ∣ 5 − 2 x 3 ∣ ≤ − 8 4 - 2\left|\frac{5 - 2x}{3}\right| \le -8 4 − 2 3 5 − 2 x ≤ − 8 81 Question bank First Midterm 1441H S2, Q1 A Classify each of the following numbers into rational or irrational: { − 8 3 , 3.17 6 , ( 2 + 5 ) 2 , 1.3 4 ‾ , 5 + 16 , csc ( π 6 ) , π 2 } \left\{\sqrt[3]{-8}, \frac{3.17}{6}, \left(\sqrt{2} + \sqrt{5}\right)^2, 1.3\overline{4}, \sqrt{5 + \sqrt{16}}, \csc\left(\frac{\pi}{6}\right), \frac{\pi}{2}\right\} { 3 − 8 , 6 3.17 , ( 2 + 5 ) 2 , 1.3 4 , 5 + 16 , csc ( 6 π ) , 2 π } 82 Question bank First Midterm 1441H S2, Q1 B(i) Solve the inequality and write your answer in interval notation: 4 + 3 ( 2 x − 1 ) ≥ x + 2 4 + 3(2x - 1) \ge x + 2 4 + 3 ( 2 x − 1 ) ≥ x + 2 83 Question bank First Midterm 1441H S2, Q1 B(ii) Solve the inequality and write your answer in interval notation: 3 ≤ ∣ x + 1 ∣ < 9 3 \le |x + 1| < 9 3 ≤ ∣ x + 1∣ < 9 84 Question bank First Midterm 1441H S2, Q2 C Rewrite the expression ∣ 6 x − 2 ∣ |6x - 2| ∣6 x − 2∣ without the absolute value.