In previous lessons we have worked on and practiced solving algebraic equations. Algebraic
equations have a variable and an equal sign. These equations had a common characteristic: Each
equation had exactly one solution. In contrast, inequalities can have multiple solutions.
When you use an expression such as at least or at most, you are talking about an inequality. For
example, if you had $20 in your pocket when you went shopping, you could spend at most $20. You
could spend exactly $20 or you could spend less than $20, but you could not spend more than $20. In
math terms, we use symbols such as < or > when working inequalities. Below is a list of the different
symbols used to show inequalities:
Inequalities can contain variables, as in x > 2. A solution of an inequality is any value that makes
the inequality true. For example, 7, 8 and 15 are solutions of x > 6 because each number is greater than
For some inequalities, there are an infinite amount of solutions. Since it is impossible to list an
infinite number of solutions, a number-line graph is used as a means of picturing them.
Application to Real Life: To be labeled sugar free, a good product must contain less than 0.5
grams of sugar per serving. Write an inequality to describe this requirement.
amount of sugaris less than0.5 grams
Let s represent the amount of sugar
s < 0.5 grams