How does the solution change when the equation becomes an inequality?
In this lesson, you will understand how to solve quadratic inequalities and represent the solution(s)
You have previously solved linear equations, linear inequalities, and quadratic equations at the end of using graphs and tables.
Given 2x − 14 = -6
This linear equation is solved by simply adding 14 to both sides and dividing by 2 to get the one value for x that would make this equation true.
2x − 14 + 14
2x
=
=
-6 + 14
8
2x 2
=
8 2
x
=
4
How does the solution change when the equation becomes an inequality?
2x – 14
2x – 14 + 14
2x
≤
≤
≤
-6
-6 + 14
8
2x 2
≤
2x 2
x
≤
4
The best way to SEE this solution and to understand that it is
an infinite set of numbers, is with a number line graph:
This number line graph indicates that the solution set is all real numbers less than 4 and including 4.
