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प्रश्न
Use the real number line to find the range of values of x for which:
–1 < x ≤ 6 and –2 ≤ x ≤ 3
उत्तर
–1 < x ≤ 6 and –2 ≤ x ≤ 3
Both the given in equations are true in the range where their graphs on the real number lines overlap.
The graphs of the given in equations can be drawn as:
–1 < x ≤ 6
–2 < x ≤ 3
From both graphs, it is clear that their common range is –1 < x ≤ 3
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संबंधित प्रश्न
Solve the following inequation, write the solution set and represent it on the number line `-x/3 <= x/2 - 1 1/3 < 1/6, x ∈ R`
Illustrate the set {x : –3 ≤ x < 0 or x > 2; x ∈ R} on the real number line.
Find the range of values of x, which satisfy:
`- 1/3 <= x/2 + 1 2/3 < 5 1/6`
Graph in each of the following cases the values of x on the different real number lines:
- x ∈ W
- x ∈ Z
- x ∈ R
Given that x ∈ I. solve the inequation and graph the solution on the number line:
`3 >= (x - 4)/2 + x/3 >= 2`
Given:
A = {x : 11x – 5 > 7x + 3, x ∈ R} and
B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}.
Find the range of set A ∩ B and represent it on the number line.
Solve the following in equation and write the solution set:
13x - 5 < 15x + 4 < 7x + 12, x ∈ R
Represent the solution on a real number line.
Solve the following inequation, write the solution set and represent it on the number line.
`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`
Solve the following inequation and graph the solution on the number line.
`-2(2)/(3) ≤ x + (1)/(3) < 3(1)/(3); x ∈ "R"`
Solve the following inequalities and represent the solution on a number line:
`(2x + 5)/(4) > (4 - 3x)/(6)`
Given: P {x : 5 < 2x – 1 ≤ 11, x∈R)
Q{x : – 1 ≤ 3 + 4x < 23, x∈I) where
R = (real numbers), I = (integers)
Represent P and Q on number line. Write down the elements of P ∩ Q.
