Advertisements
Advertisements
Question
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.
Solution
A = {x : –8 < 5x + 2 ≤ 17, x ∈ I}
= {x : –10 < 5x ≤ 15, x ∈ I}
= {x : –2 < x ≤ 3, x ∈ I}
It can be represented on number line as
B = {x : –2 ≤ 7 + 3x < 17, x ∈ R}
= {x : –9 ≤ 3x < 10, x ∈ R}
= {x : –3 ≤ x < 3.33, x ∈ R}
It can be represeneted on number line as
A ∩ B = {–1, 0, 1, 2, 3}
APPEARS IN
RELATED QUESTIONS
Solve the following inequation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Represent the solution on a real number line.
Represent the following inequalities on real number line:
2(2x – 3) ≤ 6
P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 ≥ 5(x – 5); where x ∈ R. Represent:
- P ∩ Q
- P – Q
- P ∩ Q’ on the different number of lines.
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 `(3x)/(5) - (2x - 1)/(3)` > 1, x ∈ R and represent the solution set on the number line.
Solving the following inequation, write the solution set and represent it on the number line. – 3(x – 7)≥15 – 7x > `(x + 1)/(3)` , n ∈R
Solve the inequation : `-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`. Graph the solution set on the number line.
Solve the following inequation and represent the solution set on the number line : `4x - 19 < (3x)/(5) - 2 ≤ -(2)/(5) + x, x ∈ "R"`
Find the solution set of the inequation x + 5 < 2 x + 3 ; x ∈ R Graph the solution set on the number line.
Solve the following inequation. Write down the solution set and represent it on the real number line.
–5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R
