Advertisements
Advertisements
प्रश्न
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 a number line
उत्तर
A = {x : 11x – 5 > 7x + 3, x ∈R}
B = {x : 18x – 9 ≥ 15 + 12x, x ∈R}
Now, A = 11x – 5 > 7x + 3
⇒ 11x – 7x > 3 + 5
⇒ 4x > 8
⇒ x > 2, x ∈ R
B = 18x - 9 ≥ 15 + 12x
⇒ 18x - 12x ≥ 15 + 9
⇒ 6x ≥ 24
⇒ x ≥ 4
∴ A ∩ B = x ≥ 4, x ∈ R
Hence Range of A ∩ B = {x : x ≥ 4, x ∈ R} and its graph will be.
APPEARS IN
संबंधित प्रश्न
Solve the following inequation, write down the solution set and represent it on the real number line:
–2 + 10x ≤ 13x + 10 < 24 + 10x, x 𝜖 Z
Solve the following inequation and represent the solution set on the number line:
4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R
Represent the following inequalities on real number line:
– 4 < x < 4
Represent the solution of the following inequalities on the real number line:
7 – x ≤ 2 – 6x
Solve the inequation:
3z – 5 ≤ z + 3 < 5z – 9, z ∈ R.
Graph the solution set on the number line.
Solve the following inequation and write down the solution set:
11x - a <15 x + 4 ≤ 12xk + 14 , x ∈ W
Represent the solution on a real number line.
Graph the solution set for each inequality:
-3≤ x ≤3.
Find the values of x, which satisfy the inequation
`-2(5)/(6) <(1)/(2) - (2x)/(3) ≤ 2, x ∈ "W"`. Graph the solution set on the number line.
Solve x – 3 (2 + x) > 2 (3x – 1), x ∈ { – 3, – 2, – 1, 0, 1, 2, 3}. Also represent its solution on the number line.
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.
