Advertisements
Advertisements
प्रश्न
Solve the following inequalities and graph their solution set:
`(x + 8)/(x + 1) > 1`.
उत्तर
The inequality `(x + 8)/(x + 1) > 1` is equivalent to
`(x + 8)/(x + 1) - 1 > 0 ⇔ (x + 8 - x - 1)/(x + 1) > 0`
⇒ `(7)/(x + 1)`
= 0
but `(a)/(b) > 0, a > 0 ⇔ b > 0`
Thus, `(7)/(x + 1) > 0, 7 > 0`
⇒ x + 1 > 0 or x > -1
The graph of this set is
APPEARS IN
संबंधित प्रश्न
`x < -y => -x > y`
Represent the solution of the following inequalities on the real number line:
1 + x ≥ 5x – 11
If 5x – 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.
Solve and graph the solution set of:
2x – 9 ≤ 7 and 3x + 9 > 25, x ∈ I
Solve and graph the solution set of:
5 > p – 1 > 2 or 7 ≤ 2p – 1 ≤ 17, p ∈ R
Solve for x in the following in-equation, if the replacement set is R;
9 - 4x ≤ 15 - 7x
Solve for x : 2x + 7 ≥ 5x - 14, where x is a positive prime number.
Solve the following inequalities in the given universal set:
2x - 5 ≤ 5x + 4 < 11, where x ∈ I.
Find the solution set of the following inequalities and draw the graph of their solutions sets:
| 3 - 2x | ≥ 2
The minimum value of x for the inequation 5x – 4 ≥ 18 – 6x is ______.
