Advertisements
Advertisements
Question
Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.
Solution
2x – 5 ≤ 5x + 4 < 11 2x – 5 ≤ 5x + 4
⇒ 2x – 5 – 4 ≤ 5x and 5x + 4 < 11
⇒ 2x – 9 ≤ 5x and 5x < 11 – 4
and 5x < 7
⇒ 2x – 5x ≤ 9 and x < `(7)/(5)`
⇒ 3x > – 9 and x< 1.4
⇒ x > – 3
APPEARS IN
RELATED QUESTIONS
Represent the following inequalities on real number line:
– 2 ≤ x < 5
Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}
Represent on different number lines:
A' ∩ B
Solve the following inequation and represent the solution set on the number line 2x – 5 ≤ 5x + 4 < 11, where x ∈ I.
Solve the following linear in-equation and graph the solution set on a real number line:
`1/3 (5"x" - 8) >= 1/2 (4"x" - 7) `, x ∈ R
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 > (2(3 - 4x))/(7) ≥ - 2`.
Solve the following inequation and graph the solution on the number line. `-2(2)/(3) ≤ x + (1)/(3) < 3 + (1)/(3)`x∈R
Solve `(2x + 1)/(2) + 2(3 - x) ≥ 7, x ∈ "R"`. Also graph 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
The real number lines for two inequations A and B are as given below, A ∩ B is:
