Worksheet on Linear Inequations



Worksheet on linear inequations will help the student to practice different questions on inequalities. To practice this sheet student can recall this topic to solve linear inequation, find the solution and represent the solution set of an inequation on the real line.



1. Write the word statement for each of the following inequations:

  (a) x > -5
  (b) x > 7
  (c) x < -2
  (d) x < 3
  (e) x ≥ 6
  (f) x ≥ -8
  (g) x ≤ 9
  (h) x ≤ -11


2. Write the resulting equation in each of the following cases when each side of the equation:

  (a) x > -2 is increased by 4
  (b) x < 5 is increased by 2
  (c) -x > 7 is increased by 3
  (d) -x < -4 is increased by 5
  (e) x ≤ -4 is decreased by 1
  (f) x - 7 ≥ -5 is increased by 3
  (g) -x/5 > -3 is multiplied by -3
  (h) -x > 27 is divided by 9
  (i) 4x ≤ -12 is divided by -4
  (j) x < -9 is divided by 3
  (k) -x ≤ 4 is multiplied by -6


3. Draw the separate number line for the ‘following inequations’.

  (a) x < 3, x ∈ N
  (b) 3 ≤ x < 6, x ∈ N
  (c) 0 < x < 7, x ∈ W
  (d) x ≥ 12, x ∈ W
  (e) -5 < x, ≤ 5, x ∈ I
  (f) x < -9, x ∈ I


4. Draw a separate number line for the inequation -5 < x ≤ 4 when

    (a) x ∈ N         (b) x ∈ W         (c) x ∈ I

Write the replacement set and solution set in each case.

5. Solve the following inequations and represent them graphically

  (a) x - 6 < 4, x ∈ W
  (b) x + 4 ≤ 8, x ∈ N
  (c) 9x - 6 ≥ 12, x ∈ N
  (d) -5 < x < 5, x ∈ I
  (e) 6x + 2 ≤ 20, x ∈ W
  (f) 7x + 2 < -12, x ∈ I
  (g) x - 10 > -1, x ∈ I
  (h) -2 ≤ x ≤ 2, x ∈ I
  (i) 3x + 6 > 12, x ∈ W
  (j) 7x + 3 < 5x + 9, x ∈ W
  (k) (3x - 4)/2 ≥ (x + 1)/4 - 1, x ∈ N
  (l) x/3 > x/2 + 1, x ∈ W
  (m) 2(2x + 3) - 10 < 6x(x - 2), x ∈ I
  (n) 3x - 7 > 5x - 1, x ∈ I

Try to answer the questions of the worksheet on linear inequations and represent the solution set of an inequation on the number line.



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