Q. 15

# Solve each of the

Given and 2(2x + 3) < 6(x – 2) + 10

Let us consider the first inequality.

3(2x – 11) ≥ 4(4x – 18)

6x – 33 ≥ 16x – 72

6x – 33 + 33 ≥ 16x – 72 + 33

6x ≥ 16x – 39

16x – 39 ≤ 6x

16x – 39 + 39 ≤ 6x + 39

16x ≤ 6x + 39

16x – 6x ≤ 6x + 39 – 6x

10x ≤ 39

(1)

Now, let us consider the second inequality.

2(2x + 3) < 6(x – 2) + 10

4x + 6 < 6x – 12 + 10

4x + 6 < 6x – 2

4x + 6 – 6 < 6x – 2 – 6

4x < 6x – 8

6x – 8 > 4x

6x – 8 + 8 > 4x + 8

6x > 4x + 8

6x – 4x > 4x + 8 – 4x

2x > 8

x > 4

x (4, ∞) (2)

From (1) and (2), we get

x

Thus, there is no solution of the given system of inequations.

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