30-Day Linear Inequations Practice Plan with Solutions (ICSE Class 10)
Solve: 3x - 7 < 2x + 5, where x ∈ ℝ.
Solution:
3x - 7 < 2x + 5
⇒ 3x - 2x < 5 + 7 ⇒ x < 12
Hence, solution: x < 12, x ∈ ℝ.
Day 2 (PYQ):
Solve: (5x - 3)/2 ≥ 7, x ∈ ℤ.
Solution:
(5x - 3)/2 ≥ 7 ⇒ 5x - 3 ≥ 14 ⇒ 5x ≥ 17 ⇒ x ≥ 17/5 = 3.4
Integer solutions: x ≥ 4.
Day 3:
Solve: -3 ≤ 2x - 1 < 5, x ∈ ℝ.
Solution:
Add 1: -2 ≤ 2x < 6 ⇒ Divide by 2: -1 ≤ x < 3.
Hence, x ∈ [-1, 3).
Day 4:
Solve: 4(2x - 3) ≤ 3(3x + 2), x ∈ 𝕎.
Solution:
8x - 12 ≤ 9x + 6 ⇒ -12 - 6 ≤ 9x - 8x ⇒ -18 ≤ x ⇒ x ≥ -18.
x ∈ 𝕎 ⇒ smallest x = 0.
Day 5 (PYQ):
Solve: (2x + 3)/5 < 4, x ∈ ℝ.
Solution:
2x + 3 < 20 ⇒ 2x < 17 ⇒ x < 8.5.
Day 6:
Solve: 6x - 9 > 3x + 6, x ∈ ℕ.
Solution:
6x - 3x > 6 + 9 ⇒ 3x > 15 ⇒ x > 5.
x ∈ ℕ ⇒ x ≥ 6.
Day 7:
Solve: -5 < 2x + 1 ≤ 7, x ∈ ℤ.
Solution:
-6 < 2x ≤ 6 ⇒ Divide by 2: -3 < x ≤ 3.
Integer solutions: -2, -1, 0, 1, 2, 3.
Day 8 (PYQ):
Solve: -4x + 7 ≤ 2x - 5, x ∈ ℝ.
Solution:
-4x - 2x ≤ -5 - 7 ⇒ -6x ≤ -12 ⇒ x ≥ 2.
Day 9:
Solve: (x - 5)/3 ≥ 2 - (x/2), x ∈ ℝ.
Solution:
Multiply by 6: 2(x - 5) ≥ 12 - 3x ⇒ 2x - 10 ≥ 12 - 3x ⇒ 5x ≥ 22 ⇒ x ≥ 22/5 =
4.4.
Day 10:
Solve: 1 ≤ 3x - 2 < 10, x ∈ ℕ.
Solution:
Add 2: 3 ≤ 3x < 12 ⇒ x ∈ [1, 3).
Natural numbers: 1, 2, 3.
Day 11:
Solve: 3x + 2 ≤ 4(2x - 3), x ∈ ℤ.
Solution:
3x + 2 ≤ 8x - 12 ⇒ -5x ≤ -14 ⇒ x ≥ 14/5 = 2.8.
x ∈ ℤ ⇒ x ≥ 3.
Day 12:
Solve: 7 - 2x > 3(1 - x), x ∈ ℝ.
Solution:
7 - 2x > 3 - 3x ⇒ -2x + 3x > 3 -7 ⇒ x > -4.
Day 13 (PYQ):
Solve: (2x + 5)/4 < x - 1, x ∈ ℝ.
Solution:
2x + 5 < 4x - 4 ⇒ -2x < -9 ⇒ x > 4.5.
Day 14:
Solve: -8 < 5 - 3x ≤ 4, x ∈ ℤ.
Solution:
Subtract 5: -13 < -3x ≤ -1 ⇒ Multiply -1: 13 > 3x ≥ 1 ⇒ 1 ≤ 3x < 13 ⇒
x ∈ [1/3, 13/3).
Integers: x = 1, 2, 3, 4.
Day 15:
Solve: (4x - 3)/2 ≥ (3x + 5)/3, x ∈ ℝ.
Solution:
Cross multiply: 3(4x - 3) ≥ 2(3x + 5) ⇒ 12x -9 ≥ 6x +10 ⇒ 6x ≥ 19 ⇒ x ≥ 19/6 ≈
3.17.
Day 16 (PYQ):
A number is greater than 2 but ≤ 9, x ∈ ℕ.
Solution:
2 < x ≤ 9 ⇒ x = 3,4,5,6,7,8,9.
Day 17:
Solve: 8 - 3x < 2x + 13, x ∈ ℝ.
Solution:
-5x < 5 ⇒ x > -1.
Day 18 (PYQ):
Solve: (x + 7)/3 > (2x - 5)/4, x ∈ ℤ.
Solution:
4(x + 7) > 3(2x -5) ⇒ 4x +28 > 6x -15 ⇒ -2x > -43 ⇒ x < 21.5.
Day 19:
Solve: -10 ≤ 4x - 6 < 2, x ∈ ℕ.
Add 6: -4 ≤ 4x < 8 ⇒ Divide: -1 ≤ x < 2.
Natural numbers: 1.
Day 20:
Solve: 3(2x - 4) ≤ 5x + 1, x ∈ ℝ.
6x -12 ≤ 5x +1 ⇒ x ≤ 13.
Day 21 (PYQ):
Solve: 7x - 9 ≤ 5x + 3, x ∈ ℕ.
2x ≤ 12 ⇒ x ≤ 6.
Natural numbers: 1,2,3,4,5,6.
Day 22:
Solve: 0 < (2x + 3)/5 ≤ 3, x ∈ ℝ.
0 < 2x + 3 ≤ 15 ⇒ -3 < 2x ≤12 ⇒ -1.5 < x ≤6.
Day 23:
Solve: (2x - 3)/5 ≥ (x + 4)/3, x ∈ ℝ.
6x -9 ≥ 5x +20 ⇒ x ≥29.
Day 24 (PYQ):
Solve: 9x + 2 > 3(2x +5), x ∈ ℤ.
9x +2 > 6x +15 ⇒ 3x >13 ⇒ x >13/3 ≈4.33.
Day 25:
Solve: 3x - 4 ≤ 2(2x +1), x ∈ 𝕎.
3x -4 ≤4x +2 ⇒ -x ≤6 ⇒ x ≥ -6.
Whole numbers: x ≥ 0.
Day 26:
Solve: -3 ≤ (4x -1)/2 < 5, x ∈ ℕ.
Multiply 2: -6 ≤ 4x -1 <10 ⇒ -5 ≤ 4x <11 ⇒ -1.25 ≤ x <2.75.
Natural numbers: 1,2.
Day 27 (PYQ):
Solve: -x +5 > 2x -4, x ∈ ℝ.
-x -2x > -4 -5 ⇒ -3x > -9 ⇒ x <3.
Day 28:
Solve: 2(3x -2) ≥5(x -3), x ∈ ℕ.
6x -4 ≥5x -15 ⇒ x ≥ -11.
Natural numbers: x ≥1.
Day 29:
Solve: -6 < x +3 <9, x ∈ ℝ.
-9 < x <6.
Day 30 (PYQ):
A number lies between -4 and 6 (inclusive), x ∈ ℤ.
-4 ≤ x ≤6 ⇒ Integers: -4,-3,-2,-1,0,1,2,3,4,5,6.