Advertisements
Advertisements
प्रश्न
Solve the inequation : `(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ 1(3)/(5) + (3x - 1)/(7), x ∈ "R"`
उत्तर
`(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ 1(3)/(5) + (3x - 1)/(7)`
`(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ (8)/(5) + (3x - 1)/(7)`
Multiplying by L.C.M. of 7 and 5 i.e. 35
25x + 5 - 4 (5x + 14) ≤ 56 + 15x - 5
25x + 5 - 20x - 56 ≤ 56 - 5 - 5 + 56
25x - 20x - 15x ≤ 56 - 5 - 5 + 56
-10x ≤ 102
-x ≤`(102)/(10)`
⇒ -x ≤ `(51)/(5)`
⇒ x ≥ - `(51)/(5)`
∵ x ∈ R
∴ Solution set = `{x : x ∈ "R", x ≥ - (51)/(5)}`
APPEARS IN
संबंधित प्रश्न
Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is at most 20.
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 : -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 - 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
Solve: `(2x - 3)/(4) ≥ (1)/(2)`, x ∈ {0, 1, 2,…,8}
`(2x + 3)/(3) ≥ (3x - 1)/(4)` where x is positive even integer.
Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N
If P is the solution set of – 3x + 4 < 2x – 3, x ∈ N and Q is the solution set of 4x – 5 < 12, x ∈ W, find
(i) P ∩ Q
(ii) Q – P.
If x ∈ W, then the solution set of the in equation 5 – 4x ≤ 2 – 3x is ______.
x(8 – x) > 0 and x ∈ N gives ______.
