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in Linear Equations by (15.7k points)
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 Solve the following systems of linear in equations:

\(\frac{7{\text{x}} - 1}{2}\) < -3, \(\frac{{\text{x}} + 8}{5}\) + 11 < 0

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1 Answer

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\(\frac{7{\text{x}} - 1}{2}\) < -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

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