Linear Inequalities

Question 8: Given that 3< x−2 <4 and x is an integer. List all the possible values of x. Solution: 3< x−2 <4 3 2 <x−2< 4 2 9<x−2 x>11   or   x−2<16 x<18 11<x<18 x=12, 13, 14, 15, 16, 17 Question 9: Find the biggest and the smallest integer of x that satisfy 3x + 2 ≥ –4 and 4 – x > 0. Solution: 3x + 2 ≥ –4 3x ≥ –4 – … Read more

Question 5: Solve each of the following inequalities. (a) 3x + 4 > 5x – 10 (b)   –3  ≤ 2x + 1 < 7 Solution: (a) 3x + 4 > 5x – 10 3x – 5x > –10 – 4 –2x > –14 –x > –7 x < 7 (b) –3 ≤ 2x + 1 … Read more

7.2.1 Linear Inequalities, PT3 Focus Practice Question 1: Draw a number line to represent the solution for the linear inequalities –3 < 5 – x  ≤ 4.   Solution: –3 < 5 – x   and   5 – x  ≤ 4 x < 5 + 3   and   –x  ≤ 4 – 5 x … Read more

7.1.4 Solve Inequalities in One Variable To solve linear inequalities in one variable, use inverse operation to make the variable as the subject of the inequality. Example: Solve the following linear inequalities. (a) 3−2x<1 (b)  5−2x 3 ≤7 Solution: (a)  3−2x<1 3−2x−3<1−3    −2x<−2    2x>2    2x 2 > 2 2  x>1 (b) 5−2x 3 ≤7 ( … Read more

7.1 Linear Inequalities 7.1.1 Inequalities 1.   To write the relationship between two quantities which are not equal, we use the following inequality signs:   > greater than   < less than   ≥ greater than or equal to   ≤ less than or equal to 2.   7 > 4 also means 4 < … Read more