Advertisements
Advertisements
Question
Solve the following inequation, write down the solution set and represent it on the real number line:
–2 + 10x ≤ 13x + 10 < 24 + 10x, x ๐ Z
Solution
Given inequation: –2 + 10x ≤ 13x + 10 < 24 + 10x, x ๐ Z
⇒ `-2 + 10x <= 13x + 10` and 13x + 10 < 24 + 10x
⇒ `-2 - 10 <= 13x - 10x` and 13x - 10x < 24 - 10
⇒ `-12 <= 3x` and 3x < 14
⇒ `-4 <= x` and x < 4.6
∴ Solution set {x : 4 x 4.6 and x ∈ Z)
Representation on number line is as follows:
APPEARS IN
RELATED QUESTIONS
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 solution of the following inequalities on the real number line:
x + 3 ≤ 2x + 9
Represent the solution of the following inequalities on the real number line:
`(2x + 5)/3 > 3x - 3`
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.
Find the set of values of x, satisfying:
`7x + 3 >= 3x - 5` and `x/4 - 5 <= 5/4 -x`, where x ∈ N
Solve:
`(2x + 3)/3 >= (3x - 1)/4`, where x is a positive even integer
Solve the inequation:
`-2 1/2 + 2x <= (4x)/5 <= 4/3 + 2x, x ∈ W`.
Graph the solution set on the number line.
Solve the following inequalities and represent the solution on a number line:
3x + 4 ≤ x + 8
Solve the following inequalities and represent the solution set on a number line:
`0 < (3x - 2)/(4) ≤ 2`
If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.
