Question

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

Answer 1

Given :     5(2x – 7) – 3(2x + 3) ≤ 0,   2x + 19 ≤ 6x + 47

To find :  represent the solution graphically on number line

Solution:

5(2x – 7) – 3(2x + 3) ≤ 0

10x - 35 - 6x - 9 ≤ 0

=> 4x  - 44 ≤ 0

=> 4x ≤ 44

=> x  ≤ 11

2x + 19 ≤ 6x + 47

=> 19 ≤ 4x + 47

=> -28 ≤ 4x

=> -7 ≤  x

=> x ≥ - 7

- 7 ≤   x  ≤ 11

Number line atached

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Answer 2

Step-by-step explanation:

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) it can be concluded that the solution set for the given system of inequalities is (−7,11).