Mathematics
5 + x ≤ 2x < x - 2, x ∈ R.
Statement (1) : There is no value of x ∈ R that satisfies the given inequation.
Statement (2) : 5 + x - x ≤ 2x - x < x - 2 - x ⇒ 5 ≤ x < -2
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1 is false, and statement 2 is true.
Reason
Given,
5 + x ≤ 2x
⇒ 5 ≤ 2x - x
⇒ 5 ≤ x ………. (1)
And, 2x < x - 2
⇒ 2x - x < -2
⇒ x < -2 ………. (2)
From (1) and (2), we get
⇒ 5 ≤ x < -2
From solving the above inequation, we get a solution set for x. So, statement 1 is false and statement 2 is true.
Hence, option 4 is correct.
Related Questions
Inequation 5 - 2x ≥ x - 10, where x ∈ N (Natural numbers)
Assertion (A): 5 - 2x ≥ x - 10 ⇒ -3x ≥ -15 ⇒ x ≥ 5
∴ Solution set = {5, 6, 7, 8, ……….}
Reason (R): 5 - 2x ≥ x - 10 ⇒ 5 + 10 ≥ 3x ⇒ x ≤ 5
∴ Solution set = {1, 2, 3, 4, 5}
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
x ∈ W, x ≥ -3 and x < 5.
Statement (1) : There will be no solution for the given inequalities.
Statement (2) : The real number line for the given inequations is :
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Given x ∈ {whole numbers}, find the solution set of :
-1 ≤ 3 + 4x < 23