Linear Inequalities

Linear inequalities are mainly used to represent:

1. Exact values only
2. Conditions and restrictions
3. Only quadratic equations
4. Geometrical shapes only

Which of the following inequalities has no solution?

1. x + 2 > x + 5
2. x > 3
3. x ≤ 10
4. 2x ≥ 4

Which interval represents x ≤ 6?

1. (6, ∞)
2. (-∞, 6]
3. [6, ∞)
4. (-∞, 6)

The solution of 4x + 3 ≥ 15 is:

1. x ≥ 3
2. x ≤ 3
3. x ≥ 12
4. x ≤ 12

If x = 4 is a solution of an inequality, which statement is true?

1. It satisfies the inequality
2. It changes the inequality sign
3. It makes the inequality impossible
4. It removes the variable

Which symbol is used to represent “less than or equal to”?

1. >
2. <
3. ≥
4. ≤

The solution of -3x < 12 is:

1. x < -4
2. x > -4
3. x < 4
4. x > 4

Which of the following is an example of a compound inequality?

1. x > 5
2. 2 < x < 7
3. x = 4
4. x + 3 = 9

The graph of x > 2 on the number line is represented by:

1. Closed circle at 2 and shading left
2. Open circle at 2 and shading right
3. Closed circle at 2 and shading right
4. Open circle at 2 and shading left

Solve the inequality 5x - 7 ≤ 18.

1. x ≤ 5
2. x ≥ 5
3. x ≤ 25
4. x ≥ 25

Which inequality represents the statement “a number is at least 10”?

1. x > 10
2. x < 10
3. x ≥ 10
4. x ≤ 10

The solution set of x + 4 < 9 is:

1. x < 5
2. x > 5
3. x < 13
4. x > 13

If both sides of an inequality are multiplied by a negative number, then:

1. The inequality sign remains unchanged
2. The inequality sign reverses
3. The inequality becomes an equation
4. The solution becomes zero

The solution of the inequality 2x + 5 > 11 is:

1. x > 3
2. x < 3
3. x > 8
4. x < 8

Which of the following represents a linear inequality?

1. x² + 2x > 5
2. 3x + 4 ≤ 10
3. xy > 6
4. 1/x < 2