Inequalities

“   INEQUALITIES  “

 The symbols for inequalities are 4:     < , >, ≤ , ≥

 X < 4, means  “x less than 4”

 y > 7, means “y is greater than 7”

 Z ≤ 10, means “z is less than or equal to 10”

T ≥ -3, means “T is greater than or equal to -3”

Important tip:

We follow the same procedure used for solving equations except that when we multiply or divide by a negative number the inequality is    reversed 

ex: ( 4 > -2)(-2) = -8< 4

Examples:

Solve:

 5x + 7 < 3(x + 1)  First you have to  multiply through on the right-hand side, and

                               then solve as usual:

5x + 7 < 3(x + 1)
5x + 7 < 3x + 3            *multiply 3 by each factor inside parenthesis.*
2x + 7 < 3                    *3x pass to the left side as -3x, so 5x-3x = 2x*
      2x < –4                  *Then 7 pass to the right side as -7, so -7+3 = -4 *                 
        x < –2                 * pass dividing to the right side, so -4/2 = -2*

Since I divided through by a positive "2" to get the final answer, I didn't have to flip the inequality sign.

   x-3 > 10                                                       

       x > 10 + 3

       x > 13

  2 (y-2)  ≥  3 (8-2y)

    2y – 4   ≥  24 – 6y

   2y + 6y ≥  24 + 4

      

         8y   ≥  28

          

            y  ≥ 28/8

        

             y ≥ 7/2 

"Click here to see more examples" 

Algebra 1 Solving Inequalities 6.1 - TeacherTube