Advertisements
Advertisements
Question
Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9}, find the values of x for which -3 < 2x – 1 < x + 4.
Solution
3 < 2x – 1 < x + 4.
⇒ – 3 < 2x – 1 and 2x – 1 < x + 4
⇒ – 2x < – 1 + 3 and 2x – x < 4 + 1
⇒ – 2x < 2 and x < 5
⇒ – x < 1
⇒ x > – 1
– 1 < x < 5
x ∈ {1, 2, 3, 4, 5, 6, 7, 9}
Solution set = {1, 2, 3, 4}.
APPEARS IN
RELATED QUESTIONS
If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines:
Q' ∩ P
If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines:
P-Q
If P = {x : 7x - 2 > 4x + 1, x ∈ R} and Q = {x : 9x - 45 ≥ 5 (x -5),x ∈ R} , represent the following solution set on different number lines:
P ∩ Q'
If P = {x : 7x - 4 > 5x + 2, x ∈ R} and Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}, represent the following solution set on different number lines:
P ∩ Q
If x is a negative integer, find the solution set of `(2)/(3) + (1)/(3)` (x + 1) > 0.
Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9} solve x – 3 < 2x – 1.
List the solution set of `(11 - 2x)/(5) ≥ (9 - 3x)/(8) + (3)/(4)`, x ∈ N
`x/(2) + 5 ≤ x/(3) + 6` where x is a positive odd integer.
If x ∈ { – 3, – 1, 0, 1, 3, 5}, then the solution set of the inequation 3x – 2 ≤ 8 is
Solve the inequation : `(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ 1(3)/(5) + (3x - 1)/(7), x ∈ "R"`
