Question

Assertion (A): If 2x – 5 ≤ 5x + 4 < 11, x ∈ I, then the greatest value of x is 1.

Reason (R): Adding or subtracting a negative integer to each side of an inequation does not change the inequality.

Options

• A is true, R is false

• A is false, R is true

• Both A and R are true

• Both A and R are false

Answer 1

Both A and R are true

Explanation:

Solve 2x – 5 ≤ 5x + 4 < 11:

From 2x – 5 ≤ 5x + 4

⇒ –3x ≤ 9

⇒ x ≥ –3 

From 5x + 4 < 11

⇒ 5x < 7

⇒ `x < 7/5 = 1.4` 

With x an integer, possible x are –3, –2, –1, 0, 1, so the greatest value is 1 (Assertion true).

Reason is true because adding or subtracting the same number (even a negative integer) to both sides of an inequality does not change the inequality sign.