How To Solve Compound Inequalities

Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

SIGN UP FOR A FREE TRIAL




We have learned about the simple linear inequality like an x + b > c but sometimes the inequality may be like      d < an x + b < d.

Examples of compound inequalities: - 
·          1 < 2 x + 3 < 3
·         -2 ≥ 4 x + 5 ≥ 5
·          x + 3 > 4 x > 5 x – 5
·        -2 ≤ 5 x + 9 ≤ 9
 

How to solve compound inequalities: -
 

Question 1: - If 1 < 2 x + 3 < 3, then find x.
 
Solution: -
i)  Separate the inequality like
    1 < 2 x + 3                        and     2 x + 3 < 3
 
ii)  Solve each of these inequalities separately like a simple linear inequality.
     1 < 2 x + 3
     1 – 3 < 2 x + 3 – 3
      2 < 2 x
      2 / 2 < 2 x / 2
      1 < x
 
     And 2 x + 3 < 3
     2 x + 3 – 3 < 3 – 3
     2 x < 0
     2 x / 2 < 0 / 2
     x < 0
 
     Therefore, –1< x<0.
 


Question 2: - If x + 3 > 4 x > 5 x - 5, find x.
 
Solution: -
i)   x + 3 > 4 x
     x + 3 – x > 4 x – x
     3 > 3 x
     3 / 3 > 3 x / 3
     1 > x
 
ii)   4 x > 5 x - 5
      4 x – 5 x > 5 x - 5 – 5x
      x  > -5
      x < 5
 
Therefore, 1  


 

HAVE A QUESTION? Chat With Our Tutoring Experts Now