Advertisements
Advertisements
प्रश्न
Solve the following inequation and represent the solution set on the number line:
4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R
उत्तर
The Given inequation is
`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x`, x ∈ R
`=> (4x - 19) < (3x - 10)/5 <= (-2 + 5x)/5`
`=> 5(4x - 19) < 3x - 10 < -2 + 5x`
`=> 20x - 95 < 3x - 10 <= -2 + 5x`
Solving `20x - 95 < 3x - 10`
`=> 17x < 85`
`=> x < 5`
Solving 3x - 10 <= -2 + 5x
`=> -2x <= 8`
`=> -x <= 4`
`=> x >= -4`
So the solution set = `{x : -4 <= x < 5, x in R}`
Representation on the Number line
APPEARS IN
संबंधित प्रश्न
Represent the following inequalities on real number line:
2(2x – 3) ≤ 6
Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}
Represent on different number lines:
A – B
Find the set of values of x, satisfying:
`7x + 3 >= 3x - 5` and `x/4 - 5 <= 5/4 -x`, where x ∈ N
Given:
P = {x : 5 < 2x - 1 ≤ 11, x ∈ R}
Q = {x : -1 ≤ 3 + 4x < 23, x ∈ R}
Where R = (real number), I = (Integers) Reperesnr P and Q on number lines. Write down the elements of P ∩ Q.
Solve the following inequalities and represent the solution on a number line:
2x + 3 < 5
Given that x ∈ I, solve the inequation and graph the solution on the number line: `3 ≥ (x - 4)/(2) + x/(3) ≥ 2`
Solve 2 ≤ 2x – 3 ≤ 5, x ∈ R and mark it on number line.
Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.
If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.
For the inequations A and B [as given above in part (d)], A ∪ B is:
