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प्रश्न
Solve the following inequalities and represent the solution set on a number line:
`3 > (2(3 - 4x))/(7) ≥ - 2`.
उत्तर
The given inequality `3 > (2(3 - 4x))/(7) ≥ - 2`
which is equivalent to
⇒ 3 x 7 > 2(3 - 4x) ≥ -2 x 7
⇒ `(21)/(2) > 3 - 4x ≥ - 7`
⇒ `-3 + (21)/(2) > -4x ≥ -7 -3`
⇒ `(15)/(2) > -4x ≥ - 10`
we divide this compound inequality by - 4 and reverse the inequality signs to obtain
`(15)/(2 xx (-4)) < x ≤ (-10)/(-4)`
⇒ `(15)/(-8) < x ≤ (5)/(2)`
The graph of this set is `(-15)/(8) < x ≤ (5)/(2)`.
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संबंधित प्रश्न
Represent the solution of the following inequalities on the real number line:
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Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}
Represent on different number lines:
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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 inequation and represent the solution set on the number line:
`-3 < -1/2 - (2x)/3 ≤ 5/6, x ∈ R`
Solve the following in equation write the solution set and represent it on the number line:
`-x/3 <= x/2 -1 1/3 < 1/6, x ∈ R`
Solve the following in equation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Given:
P = {x : 5 < 2x - 1 ≤ 11, x ∈ R}
Q = {x : -1 ≤ 3 + 4x < 23, x ∈ R}
Where R = (real number), I = (Integers) Reperesnr P and Q on number lines. Write down the elements of P ∩ Q.
If x ∈ W, find the solution set of `(3)/(5)x - (2x - 1)/(1) > 1` Also graph the solution set on the number line, if possible.
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.
For the inequations A and B [as given above in part (d)], A ∪ B is:
