Solving Inequalities

In order to solve an equation we must bring the variable to one side of the equation by itself. 3x + 2 = 11 is solved when we say x = 3.
 
To SOLVE AN INEQUALITY we must also bring the variable to one side of the inequality by itself.
 
Consider:

 x + 5 > 9

This is equivalent to

 x + 5 - 5 > 9 - 5 or
 x > 4

The inequality is solved in the final expression because the variable is by itself on one side.
 
To solve inequalities we can use the rules we learned previously.
 

• For x + a < c:

  x + a - a < c - a or
  x < c - a
  

• For x - a < c:

  x - a + a < c + a or
  x < c + a
  

• For 4x < c:

  4x/4 < c/4 or
  x < c/4
  

• For 7 > -2x:

  7/-2 < -2x/-2 or
  -7/2 < x

When we multiply or divide both sides of the inequality by a negative number, we must change the direction of the inequality sign.

Solve the inequality:

4x - 3 > 6

First, we add 3 to each side:

4x - 3 + 3 > 6 + 3
4x > 9

Now, to get x by itself, we divide each side by 4:

4x/4 > 9/4
x > 9/4

So our final answer is x > 9/4.