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# Solve the inequalities and represent the solution graphically on number line

5(2x - 7) - 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47

**Solution:**

5(2x - 7) - 3(2x + 3) ≤ 0

⇒ 10x - 35 - 6x - 9 ≤ 0

⇒ 4x - 44 ≤ 0

⇒ 4x ≤ 44

⇒ x ≤ 11 ....(1)

2x + 19 ≤ 6x + 47

⇒ 19 - 47 ≤ 6x - 2x

⇒ - 28 ≤ 4x

⇒ - 7 ≤ x ....(2)

From (1) and (2), we get, - 7 ≤ x ≤ 11

Hence, it can be concluded that the solution set for the given system of inequalities is [- 7, 11]

The solution of the given system of inequalities can be represented on the number line as

NCERT Solutions Class 11 Maths Chapter 6 Exercise ME Question 10

## Solve the inequalities and represent the solution graphically on number line: 5(2x - 7) - 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47

**Summary:**

Linear inequations 5(2x - 7) - 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47 is given. We have found that solution set for the given inequality is [- 7, 11]

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