# Solve each of the following system of inequations in Rx + 5 > 2(x + 1), 2 – x < 3(x + 2)

Given x + 5 > 2(x + 1) and 2 – x < 3(x + 2)

Let us consider the first inequality.

x + 5 > 2(x + 1)

x + 5 > 2x + 2

x + 5 – 5 > 2x + 2 – 5

x > 2x – 3

2x – 3 < x

2x – 3 + 3 < x + 3

2x < x + 3

2x – x < x + 3 – x

x < 3

x (–∞, 3) (1)

Now, let us consider the second inequality.

2 – x < 3(x + 2)

2 – x < 3x + 6

2 – x – 2 < 3x + 6 – 2

–x < 3x + 4

3x + 4 > –x

3x + 4 – 4 > –x – 4

3x > –x – 4

3x + x > –x + x – 4

4x > –4

x > –1

x (–1, ∞) (2)

From (1) and (2), we get

x (–∞, 3) (–1, ∞)

x (–1, 3)

Thus, the solution of the given system of inequations is (–1, 3).

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on Equations & inequations63 mins
Discussion | Miscellaneous Exercise | NCERT Chapter 6| Linear Inequalities33 mins
Concept of Linear momentum and its conservation40 mins
Check your understanding of linear momentum22 mins
Conservation of Linear Momentum, Visualize the concept (Theory + Interactive Quiz)41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses