Advertisements
Advertisements
Question
Solve the following inequation and represent the solution set on a number line.
`-8 1/2 < -1/2 - 4x ≤ 7 1/2, x ∈ I`
Solution
`-8 1/2 < -1/2 - 4x <= 7 1/2, x ∈ I`
`-8 1/2<-1/2 - 4x`
⇒ `(-17)/2<-1/2 - 4"x"`
⇒ `(-17)/2+1/2 < 4"x"`
⇒ `(-17)/2 < (- 1 - 8x)/2`
⇒ – 17 < – 1 – 8x
⇒ + 8x < – 1 + 17
⇒ 8x < 16
⇒ x < 2
`-1/2 - 4x ≤ 7 1/2`
⇒ `-1/2 - 4x ≤ 15/2`
⇒ `-4x ≤ 15/2 + 1/2`
⇒ – 4x ≤ 8
⇒ x ≥ – 2
So,
– 2 ≤ x < 2
As, `x ∈ I`
x = {–2, –1, 0, 1}
APPEARS IN
RELATED QUESTIONS
For the following inequations, graph the solution set on the real number line:
– 4 ≤ 3x – 1 < 8
Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}
Represent on different number lines:
A – B
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.
Graph the solution set for each inequality:
-3< x <5
Solve the following inequalities and represent the solution on a number line:
`(2x + 5)/(4) > (4 - 3x)/(6)`
Given that x ∈ R, solve the following inequation and graph the solution on the number line: – 1 ≤ 3 + 4x < 23.
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.
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
