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प्रश्न
Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.
उत्तर
2x – 5 ≤ 5x + 4 < 11 2x – 5 ≤ 5x + 4
⇒ 2x – 5 – 4 ≤ 5x and 5x + 4 < 11
⇒ 2x – 9 ≤ 5x and 5x < 11 – 4
and 5x < 7
⇒ 2x – 5x ≤ 9 and x < `(7)/(5)`
⇒ 3x > – 9 and x< 1.4
⇒ x > – 3
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संबंधित प्रश्न
Represent the following inequalities on real number line:
3x + 1 ≥ – 5
Represent the following inequalities on real number line:
2(2x – 3) ≤ 6
Use the real number line to find the range of values of x for which:
–1 < x ≤ 6 and –2 ≤ x ≤ 3
Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}
Represent on different number lines:
A' ∩ B
Given that x ∈ I. solve the inequation and graph the solution on the number line:
`3 >= (x - 4)/2 + x/3 >= 2`
Graph the solution set for each inequality:
x ≥ - 3
Solve the following inequalities and represent the solution on a number line:
`(3x)/(2) + (1)/(4) > (5x)/(8) - (1)/(2)`
Solve the following inequalities and represent the solution set on a number line:
`-3 < - (1)/(2) - (2x)/(3) < (5)/(6), x ∈ "R"`.
Given A = {x : x ∈ I, – 4 ≤ x ≤ 4}, solve 2x – 3 < 3 where x has the domain A Graph the solution set on the number line.
For the inequations A and B [as given above in part (d)], A ∪ B is:
