5.1A  Solving Linear Inequalities

Solving Linear Inequalities

     The idea behind solving linear inequalities is to find the solution for the variable x, and record your answer using interval notation.

Solving Compound Linear Inequalities

     Solve for x                4 ≤ 8x + 2 < 6         

    Solving any linear inequality should be done the same way as a linear equation.         

  Separate these into two inequalities                

               4 ≤ 8x + 2  AND  8x + 2 < 6

               2 ≤ 8x   AND   8x < 4

               1/4 ≤ x   AND  x < 1/2    

     If the problem is a compound linear inequality, it should be rewritten as a conjunction. 

     This is a  conjunction, so the solution set to this problem is [1/4, 1/2)