How To Solve Multi Step 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


Definition: - Inequalities which includes more than one inequality symbols is known as multi step inequalities.

 Examples of multi step inequalities: -
·        2 x + 1 < 5 x < 6 x + 9
·        5 > 3 x + 1 > 2 x – 2
·      -3 ≤ (9 x – 1) / (2 x + 3) / 9
·       30 x ≥ (x + 1) / 2 ≥ 0
 

Example 1: - Solve the following multi step inequalities and find x.
            2 x + 1 < 5 x < 9 – 6 x
 
Solution: - Solve the two inequalities separately
i)                 2 x + 1 < 5 x
                  (2 x + 1) – 1 < 5 x – 1
                   2 x < 5 x – 1
                   2 x – 5 x < (5 x – 1) – 5 x
                    -3 x < - 1
                   - 3 x / - 3 > - 1 / - 3           (If we multiply both sides by a negative number then the sign will flip.)
                  x > 1 / 3
 
ii)               5 x < 9 – 6 x
                  5 x + 6 x < (9 – 6 x) + 6 x
                  13 x < 9
                  13 x / 13 < 9 / 13
                   x < 9 / 13
Therefore 1/3  


Question 2: - 5 > 3 x + 1 > 4x + 1
 
Solution: -
i)             5>3x+1
               5-1 > 3x+1-1
               4 > 3x
               4/3 > x
 
ii)            3x+1 > 4 x + 1
               3x+1-4x > 4x + 1 -4x
                -x > 1
               X < -1
 

 
Linear FunctionsSolve Absolute Value EquationsFormula for Simple InterestFoil Methods
Foil MethodFoil MathFinding PercentFind Distance Between Two Points

View All Sub topics

HAVE A QUESTION? Chat With Our Tutoring Experts Now