## Solving Inequalities
General Explanation
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 > 9This is equivalent to x + 5 - 5 > 9 - 5 or x > 4The 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
Sample Problem
Solve the inequality:
4x - 3 > 6 Solution
First, we add 3 to each side:
4x - 3 + 3 > 6 + 3 4x > 9Now, to get x by itself, we divide each side by 4: 4x/4 > 9/4 x > 9/4So our final answer is x > 9/4. |