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
Consider the given inequation
`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R`
`=> 4x - 19 + 2 < (3x)/5 - 2 + 2 <= (-2)/5 + x + 2, x ∈ R`
`=> 4x - 17 < (3x)/5 <= x + 8/5, x ∈ R`
`=> 4x - (3x)/5 < 17 and (-8)/5 <= x - (3x)/5, x ∈ R `
`=> (20x - 3x)/5 < 17 and (-8)/5 <= (5x - 3x)/5, x ∈ R`
`=> (17x)/5 < 17 and (-8)/5 <= (2x)/5, x ∈ R`
`=> x/5 < 1` and `-4 <= x, x ∈ R`
`=> x < 5` and `-4 <= x, x ∈ R`
`=> -4 ≤ x < 5; "where" x ∈ R`
The solution set can be represented on a number line as follows:
APPEARS IN
संबंधित प्रश्न
Solve the following inequation, write down the solution set and represent it on the real number line:
–2 + 10x ≤ 13x + 10 < 24 + 10x, x 𝜖 Z
Represent the solution of the following inequalities on the real number line:
x + 3 ≤ 2x + 9
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.
Solve the following inequation and write down the solution set:
11x - a <15 x + 4 ≤ 12xk + 14 , x ∈ W
Represent the solution on a real number line.
Solve the following inequation, write the solution set and represent it on the number line:
`-x/(3) ≤ x/(2) - 1(1)/(3) < (1)/(6), x ∈ R`
Solve 2(x – 3)< 1, x ∈ {1, 2, 3, …. 10}
Solve the inequation : `-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`. Graph the solution set on the number line.
Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.
The real number lines for two inequations A and B are as given below, A ∩ B is:
