Mathematics [2 Mark Question Answer]

3x - 5 ≤ - 7, x ∈ I
3x < 5 + (-7)
3x ≤ - 2
x ≤ - 2/3
x = {......., -3, -2, -1}

2x - 4 > 3
2x > 3 + 4 ⇒ 2x > 7
x > 7 / 2 ⇒ x > 3·5
x = {4, 5 , 6, ......}

2y - 3 < y +1 ≤ 4y + 7
y - 3 < 1 ≤ 3y + 7
y < 4 and 3y ≥ - 6
y ≥ -2
-2 ≥ y < 4

The given inequality is
3(x - 2) > 1
⇒ 3x - 6 > 1
⇒ 3x > 7
⇒ x > 7/3
The graph of the solution set is given by x > 7/3.

We have the inequality
4 - 2x ≥ 6 - 3x
⇒ 3x - 2x ≥ 6 - 4
⇒ x ≥ 2
The graph of the solution set is x ≥ 2.

We have the inequality
2x - 3 > 5x + 4
⇒ -3 - 4 > 5x - 2x
⇒ -7 > 3x or x < -7/3
The graph of the solution set is x < -7/3.

We have, 3x + 4 ≤ x + 8
⇒ 3x - x ≤ 8 - 4 ...[Bring like terms on one side]
⇒ 2x ≤ 4
⇒ x ≤ 2
The graph of the solution set is x ≤ 2.

We have, 2x + 3 < 5
⇒ 2x < 5 - 3
⇒ 2x < 2
⇒ x < 1
The graph of the solution set is {x < 1}