\(\frac{7{\text{x}} - 1}{2}\) < -3
Multiplying both the sides by 2
\(\frac{7{\text{x}} - 1}{2}\)(2) < -3(2)
7x -1 < -6
Adding 6 to both the sides in above equation
7x – 1 + 6 < -6 + 6
7x + 5 < 0
Subtracting 5 from both the sides in above equation
7x + 5 – 5 < 0 – 5
7x < - 5
Dividing both the sides by 7 in above equation
Now when
\(\frac{3{\text{x}} + 8}{5}\) + 11 <0
Subtracting both the sides by 11 in the above equation
\(\frac{3{\text{x}} + 8}{5}\) + 11 - 11 < 0 - 11
\(\frac{3{\text{x}} + 8}{5}\) < -11
Multiplying both the sides by 5 in the above equation
(\(\frac{3{\text{x}} + 8}{5}\)) (5) < - 11(5)
3x + 8 < -55
Subtracting 8 from both the sides in above equation
3x + 8 – 8 < -55 – 8
3x < -63
Dividing both the sides by 3 in above equation
Therefore,
x < -21