Advertisements
Advertisements
प्रश्न
Find the solution set of the following inequalities and draw the graph of their solutions sets:
`(3)/|x - 2| > 5`.
उत्तर
We have `(3)/|x - 2| > 5`
3 > 5 | x - 2 |
5 | x - 2 | < 3
| x - 2 | < `(3)/(5)`
Using property | x | < a = -a < x < a
∴ `-(3)/(5) < x - 2 < (3)/(5)`
⇒ `-(3)/(5) + 2 < x < (3)/(5) + 2`
⇒ `(7)/(5) < x < (13)/(5)`
So `(3)/|x - 2| > 5`
⇒ `{x : (7)/(5) < x < (13)/(5)}`.
The graph of this set is
APPEARS IN
संबंधित प्रश्न
Solve the inequation:
3 – 2x ≥ x – 12 given that x ∈ N.
Find the range of values of x which satisfies
`-2 2/3 <= x + 1/3 < 3 1/3, x in R`
Graph these values of x on the number line.
Find the values of x which satisfy the inequation:
`-2 <= 1/2 - (2x)/3 ≤ 1 5/6; x ∈ N`
Graph the solution on the number line.
Solve and graph the solution set of:
x + 5 ≥ 4(x – 1) and 3 – 2x < –7, x ∈ R
Solve for x : 6 - 10x < 36, x ∈ {-3, -2, -1, O, 1, 2}
Solve for x : `"x"/4 + 3 <= "x"/3 + 4` , where xis a negative odd number.
If `(2 "x" + 7)/3 <= (5 "x" +1)/4` , find the smallest value of x, when:
(i) x ∈ R
(ii) x ∈ Z
Solve the following inequalities in the given universal set:
3x - 5 > x + 7: x ∈ N
Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.
The value of x for the inequation 3x + 15 < 5x + 13, x ∈ Z is ______.
