Sec 2 Mathematics Linear Inequalities topical questions

Write each sentence as an inequality in x.

1. (a)x is at least 12.[1]
2. (b)x is more than 12.[1]
3. (c)x is no more than 12.[1]

Number-line diagrams use circles and shading to show solutions.

1. (a)An open circle at 1 with shading to the right: write the inequality.[1]
2. (b)A closed circle at −2 with shading to the left: write the inequality.[1]
3. (c)Describe the diagram for x ≥ 3, naming the circle type and the shading direction.[1]

Solve each inequality.

1. (a)x − 7 > −2[1]
2. (b)4x ≤ 20[1]
3. (c)x/3 < 2[1]

Solve each inequality.

1. (a)x + 3 ≥ −1[1]
2. (b)5x < 35[1]
3. (c)x/4 ≤ 3[1]

Write each number-line description as an inequality, then list the integers in part (c).

1. (a)A closed circle at −1 with shading to the right.[1]
2. (b)An open circle at 4 with shading to the left.[1]
3. (c)List the integers satisfying −3 < x ≤ 2.[2]

Solve each inequality, watching for negatives.

1. (a)−3x > 12[2]
2. (b)6 − 2x ≥ 10[2]

Consider the inequality 4x + 7 < 27.

1. (a)Solve the inequality.[2]
2. (b)State the largest integer that satisfies it.[1]
3. (c)How many positive integers satisfy it?[1]

Consider the inequality 7 − 3x > −8.

1. (a)Solve the inequality.[2]
2. (b)State exactly which step caused the sign to flip, and why.[1]
3. (c)Is x = 5 a solution? Justify briefly.[1]

A number x satisfies both x > 1 and x ≤ 6.

1. (a)Write the two conditions as one statement.[1]
2. (b)List all the integers that satisfy it.[1]
3. (c)State the smallest and the largest integer solutions.[2]

Solve the inequality 3(2 − x) > 12.

Wei Xuan has $18 to spend on lunch sets costing $4.50 each, to share with friends.

1. (a)Write an inequality for n, the number of sets he can buy.[1]
2. (b)Solve the inequality.[1]
3. (c)State the greatest number of sets he can buy.[1]
4. (d)The price rises to $5. State the new greatest number of sets.[1]

A rectangle has width w cm. Its length is 3 cm more than its width, and its perimeter is at most 30 cm.

1. (a)Write an expression for the length.[1]
2. (b)Form an inequality in w for the perimeter.[1]
3. (c)Solve the inequality.[2]
4. (d)State the largest whole-number width possible.[1]

Mei has $25 in her wallet and saves $8 every week. A badminton racket costs $145, and Mei wants to have at least enough money for it.

1. (a)Form an inequality in w, the number of weeks.[2]
2. (b)Solve the inequality.[2]
3. (c)State the least number of whole weeks Mei must save.[1]

Three times a number, decreased by 5, is greater than that number increased by 4.

1. (a)Write the statement as an inequality.[1]
2. (b)Solve the inequality.[2]
3. (c)State the smallest integer satisfying it.[1]
4. (d)Show that the number 4 does not satisfy the statement.[1]

A number x must satisfy both −2x ≤ 10 and 3x + 1 < 16.

1. (a)Solve the first inequality, showing the flip.[2]
2. (b)Solve the second inequality.[1]
3. (c)Write the combined condition as one statement.[1]
4. (d)How many integers satisfy the combined condition?[1]