SOLVING LINEAR INEQUALITIES IN ONE VARIABLE WORKSHEET

Solve each of the following linear inequalities in one variables.

Problem 1 :

5x - 3 < 3x + 1

(i) when x is a real number

(ii) when x is an integer

(iii) when x is a natural number

Problem 2 : 

3x + 17 ≤ 2(1 - x)

Problem 3 :

2(2x + 3) - 10 ≤ 6(x - 2)

Problem 4 :

3x - 7 > x + 1

Problem 5 :

-(x - 3) + 4 < 5 - 2x

Problem 6 :

Problem 7 :

Problem 8 :

Problem 9 :

Problem 10 :

Answers

1. Answer :

5x - 3 < 3x + 1

2x - 3 < 1

2x < 4

x < 2

(i) When x is a real number, the solution set is

(-∞, 2)

(ii) When x is an integer, the solution set is

{...............,-4, -3, -2, - 1, 0, 1}

(iii) When x is a natural number, the solution set is

{1}

2. Answer :

3x + 17 ≤ 2(1 - x)

3x + 17 ≤ 2 - 2x

5x + 17 ≤ 2

5x ≤ -15

x ≤ -3

3. Answer :

 2(2x + 3) - 10 ≤ 6(x - 2)

4x + 6 - 10 ≤ 6x - 12

4x - 4 ≤ 6x - 12

-2x - 4 ≤ -12

-2x ≤ -8

x ≥ 4

4. Answer :

3x - 7 > x + 1

2x - 7 > 1

2x > 8

x > 4

5. Answer :

-(x - 3) + 4 < 5 - 2x

-x + 3 + 4 < 5 - 2x 

-x + 7 < 5 -2x

x + 7 < 5

x < -2

6. Answer :

x + 10 < -4

x < -14

7. Answer :

3x - 2 < -6

3x < -4

x < -⁴⁄₃

8. Answer :

3(x - 2) + 2(x + 1) > 12

3x - 6 + 2x + 2 > 12

5x - 4 > 12

5x > 16

x > ¹⁶⁄₅

9. Answer :

3(2x - 1) + 4(3x + 2) ≥ 12x + 12

6x - 3 + 12x + 8 ≥ 12x + 12

18x + 5 ≥ 12x + 12

16x + 5 ≥ 12

16x ≥ 7

x ≥ ⁷⁄₁₆

10. Answer :

-4 < 3x - 1 < 4

-3 < 3x < 4

-1 < x < ⁴⁄₃

Video Lesson

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