Question

Solve the following systems of linear in equations:

 –11 ≤ 4x – 3 ≤ 13

Answer 1

-11 ≤ 4x – 3 and 4x – 3 ≤ 13 

When,

-11 ≤ 4x - 3 4x – 3 ≥ -11 

Adding 3 to both the sides 

4x – 3 + 3 ≥ -11 + 3 

4x ≥ - 8 

Divide both the sides by 4 in above equation

\(\frac{4{\text{x}}}{4} \ge \frac{-8}{4}\)

x ≥ -2 Now 

when, 

4x – 3 ≤ 13

Adding 3 to both the sides in the above equation 

4x – 3 + 3 ≤ 13 + 3 

4x ≤ 16

Dividing both the sides by 4 in the above question

\(\frac{4{\text{x}}}{4} \le \frac{16}{4}\)

x ≤ 4

Combining the intervals: 

x ≥ -2 and x ≤ 4 

Therefore, 

x ϵ [-2, 4]