Advertisements
Advertisements
Question
Solve the inequality.
`-12 < 4 - (3x)/(-5) <= 2`
Solution
`- 12 < 4 - (3x)/(- 5) ≤ 2`
⇒ `- 12 - 4 < (-13)/(- 5) ≤ 2 - 4`
⇒ `- 16 < (3x)/5 ≤ - 2`
⇒ - 80 < 3x ≤ - 10
⇒ `(- 80)/3 < x ≤ (-10)/3`
Thus, the solution set for the given inequality is (-80/3, -10/3)
APPEARS IN
RELATED QUESTIONS
Solve 24x < 100, when x is an integer.
Solve –12x > 30, when x is a natural number.
Solve 3x + 8 > 2, when x is a real number.
Solve the given inequality for real x: 4x + 3 < 5x + 7.
Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)
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:
5x – 3 ≥ 3x – 5
Solve the given inequality and show the graph of the solution on number line:
3(1 – x) < 2 (x + 4)
Solve the given inequality and show the graph of the solution on number line:
`x/2 >= ((5x -2))/3 - ((7x - 3))/5`
Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.
Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.
Represent to solution set of each of the following inequations graphically in two dimensional plane:
x + 2y − y ≤ 0
Represent to solution set of each of the following in equations graphically in two dimensional plane:
2. x + 2y ≥ 6
Represent to solution set of each of the following inequations graphically in two dimensional plane:
4. x − 2y < 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:
0 ≤ 2x − 5y + 10
Represent to solution set of each of the following inequations graphically in two dimensional plane:
3y ≥ 6 − 2x
Represent to solution set of each of the following inequations graphically in two dimensional plane:
3x − 2y ≤ x + y − 8
Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then ______.
State whether the following statement is True or False.
If xy > 0, then x > 0, and y < 0
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.
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 ______.
Solution of a linear inequality in variable x is represented on number line given below ______.
Solution of a linear inequality in variable x is represented on number line given below ______.
If |x| > 5, then x ∈ (– `oo`, – 5) ∪ [5, `oo`)
If |x| ≤ 4, then x ∈ [– 4, 4]
