Advertisements
Advertisements
प्रश्न
Solve 3x + 8 > 2, when x is an integer.
उत्तर
The given inequality is 3x + 8 > 2.
3x + 8 > 2
⇒ 3x + 8 - 8 > 2 - 8
⇒ 3x > - 6
⇒ `(3x)/3 > (-6)/3`
⇒ x > - 2
The integers greater than –2 are –1, 0, 1, 2, …
Thus, when x is an integer, the solutions of the given inequality are –1, 0, 1, 2 …
Hence, in this case, the solution set is {–1, 0, 1, 2, …}.
APPEARS IN
संबंधित प्रश्न
Solve 24x < 100, when x is a natural number.
Solve 24x < 100, when x is an integer.
Solve –12x > 30, when x is a natural number.
Solve the given inequality for real x: 4x + 3 < 5x + 7.
Solve the given inequality for real x: 3x – 7 > 5x – 1.
Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)
Solve the given inequality for real x: x + `x/2` + `x/3` < 11
Solve the given inequality for real x: `(3(x-2))/5 <= (5(2-x))/3`
Solve the given inequality for real x: `1/2 ((3x)/5 + 4) >= 1/3 (x -6)`
Solve the given inequality for real x: 2(2x + 3) – 10 < 6 (x – 2)
Solve the given inequality for real x: 37 – (3x + 5) ≥ 9x – 8(x – 3)
Solve the given inequality and show the graph of the solution on number line:
3x – 2 < 2x +1
Solve the given inequality and show the graph of the solution on number line:
3(1 – x) < 2 (x + 4)
The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?
[Hint: If x is the length of the shortest board, then x, (x + 3) and 2x are the lengths of the second and third piece, respectively. Thus, x = (x + 3) + 2x ≤ 91 and 2x ≥ (x + 3) + 5]
Solve the inequality.
2 ≤ 3x – 4 ≤ 5
Solve the inequality.
6 ≤ –3(2x – 4) < 12
Solve the inequality.
`-3 <= 4 - (7x)/2 <= 18`
Solve the inequality.
`-12 < 4 - (3x)/(-5) <= 2`
Represent to solution set of each of the following inequations graphically in two dimensional plane:
x + 2 ≥ 0
Represent to solution set of each of the following inequations graphically in two dimensional plane:
5. −3x + 2y ≤ 6
Represent to solution set of each of the following inequations graphically in two dimensional plane:
6. x ≤ 8 − 4y
Represent to solution set of each of the following inequations graphically in two dimensional plane:
0 ≤ 2x − 5y + 10
Represent to solution set of each of the following inequations graphically in two dimensional plane:
3y ≥ 6 − 2x
State whether the following statement is True or False.
If x > 5 and x > 2, then x ∈ (5, ∞)
State whether the following statement is True or False.
If |x| < 5, then x ∈ (–5, 5)
State whether the following statement is True or False.
Graph of x > –2 is
State whether the following statement is True or False.
Solution set of x – y ≤ 0 is
The inequality representing the following graph is ______.
Solution of a linear inequality in variable x is represented on number line given below ______.
If x > –2 and x < 9, then x ∈ (– 2, 9)
