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
Given: A = {x : –8 < 5x + 2 ≤ 17, x ∈ I}, B = {x : –2 ≤ 7 + 3x < 17, x ∈ R}
Where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of 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 inequation, write the solution set and represent it on the number line.
`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`
Solve the following inequalities and represent the solution on a number line:
`(2x + 5)/(4) > (4 - 3x)/(6)`
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.
Solve the inequation 3x -11 < 3 where x ∈ {1, 2, 3,……, 10}. Also represent its solution on a number line
If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.
Solve the following inequation, write down the solution set and represent it on the real number line.
`-3 + x ≤ (7x)/2 + 2 < 8 + 2x, x ∈ I`
The solution set for the following number line is:
The number line for the solution of inequation x > 5 and x < 10 (x ∈ R) is:
