LINEAR INEQUALITIES

Solve of the following linear inequalities 
8 + 4v ≥ 20 – 2v

Solution

8 + 4v   ≥ 20 – 2v

4v + 2v ≥ 20 – 8

        6v ≥ 12

          v ≥ 12 / 6

          v ≥ 2

SOLVING LINEAR INEQUALITY 2

List all the integer values of p which satisfy both the inequalities p + 4 < 11 and  2 - 3p ≤ -7.

Solution

(i)     p + 4 <11

                    p < 11 - 4

                           p < 7              

===> 6, 5, 4, 3, 2, 1, 0, -1, -2,............

(ii)    2 - 3p ≤ -7.

              - 3p ≤ -7 -2

           - 3p ≤ - 9

                       p ≥  - 9 / -3

              p ≥  3

===> 3, 4, 5, 6, 7, 8, 9, .....................

   Compare ( i ) & ( ii )
 p = 3, 4, 5 and 6 

SOLVING LINEAR INEQUALITIES 1

Example 1

Solve the inequality  x  +  8   >  15

Solution

x  +  8  > 15

              x > 15 - 8

       x > 7

Example 2

Solve the inequality 5x  >  20

Solution

 5x  >  20

        x  >  20 / 5

 x  >  4

Example 3

Solve the inequality x / -4 ≥ 3

Solution

x/-4 ≥ 3

            x ≤ 3 (-4)

        x ≤ -12

Example 4

Solve the inequality 2x -1 ≥ 13

Solution

2x -1 ≥ 13

         2x  ≥ 13 + 1

  2x  ≥ 14

         x  ≥ 14 / 2

 x  ≥ 7

 

TIPS:

1. SAME CONCEPT AS LINEAR EQUATIONS (SAMA KONSEP SEPERTI PERSAMAAN LINEAR)

2. BUT  WHEN DIVIDED or MULTIPLIED WITH NEGATIVE NUMBER THE INEQUALITY SYMBOL WILL CHANGE         (TETAPI APABILA DIBAHAGI ATAU DIDARB DENGAN NOMBOR NEGATIF SIMBOL KETAKSAMAAN DITUKARKAN)