Advertisements
Advertisements
प्रश्न
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`
उत्तर
`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`
`\implies -3 (x - 7) ≥ 15 - 7x` and `15 - 7x > (x + 1)/3`
`\implies` –3x + 21 ≥ 15 – 7x and 45 – 21 > x + 1
`\implies` 4x ≥ –6 and 44 > 22x
`\implies x ≥ (-3)/2` and `2 > x`
`\implies` x ≥ –1.5 and 2 > x
The solution set is {x : x ∈ R, –1.5 ≤ x < 2}
The solution set is represented on number line as follows:
APPEARS IN
संबंधित प्रश्न
Represent the following inequalities on real number line:
3x + 1 ≥ – 5
Solve the inequation:
`-2 1/2 + 2x <= (4x)/5 <= 4/3 + 2x, x ∈ W`.
Graph the solution set on the number line.
Solve the following linear in-equation and graph the solution set on a real number line :
`4 3/4 >= "x" + 5/6 > 1/3` , x ∈ R
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 linear in-equation and graph the solution set on a real number line:
`5/4 "x" > 1 + 1/3 (4"x" - 1)` , x ∈ R
Give that x ∈ I. Solve the inequation and graph the solution on the number line:
`3≥(x - 4)/(2)+x/(3)≥2`
Graph the solution set for each inequality:
x ≥ - 3
Solve the following inequation and graph the solution on the number line.
`-2(2)/(3) ≤ x + (1)/(3) < 3(1)/(3); x ∈ "R"`
Solve 2(x – 3)< 1, x ∈ {1, 2, 3, …. 10}
The following number line represents:
