Advertisements
Advertisements
प्रश्न
Given that x ∈ I, solve the inequation and graph the solution on the number line: `3 ≥ (x - 4)/(2) + x/(3) ≥ 2`
उत्तर
`3 ≥ (x - 4)/(2) + x/(3) and 3 ≥ (x - 4)/(2) + x/(3) ≥ 2`
(i) `3 ≥ (3x - 12 + 2x)/(6)`
⇒ `3 ≥ (5x - 12)/(6)`
⇒ 18 ≥ 5x - 12
⇒ 5x - 12 ≤ 18
⇒ 5x ≤ 18 + 12
⇒ 5x ≤ 30
⇒ x ≤ 6
(ii) `(x - 4)/(2) + x/(3) ≥ 2`
`(3x - 12 + 2x)/(6) ≥ 2`
⇒ `(5x - 12)/(6) ≥ 2`
⇒ 5x - 12 ≥ 12
⇒ 5x ≥ 12 + 12, x ≥ `(24)/(5)`
⇒ x ≥ `4(4)/(5)`
∴ x = {5, 6}
Number line:
APPEARS IN
संबंधित प्रश्न
Given: A = {x : –8 < 5x + 2 ≤ 17, x ∈ I}, B = {x : –2 ≤ 7 + 3x < 17, x ∈ R}
Where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A ∩ B.
Find the set of values of x, satisfying:
`7x + 3 >= 3x - 5` and `x/4 - 5 <= 5/4 -x`, where x ∈ N
Solve the following linear in-equation and graph the solution set on a real number line :
`4 3/4 >= "x" + 5/6 > 1/3` , 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.
Solve the equation and represent the solution set on the number line.
`-3 + x ≤ (8x)/(3)+ 2 ≤ (14)/(3)+ 2x`, where x ∈ I
Solve the following inequalities and represent the solution on a number line:
`(2x + 5)/(4) > (4 - 3x)/(6)`
Solve the following inequalities and represent the solution set on a number line:
`-3 < - (1)/(2) - (2x)/(3) < (5)/(6), x ∈ "R"`.
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.
Solve the given inequation and graph the solution on the number line : 2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.
Solve the inequation : 5x – 2 ≤ 3(3 – x) where x ∈ { – 2, – 1, 0, 1, 2, 3, 4}. Also represent its solution on the number line.
