# What is the difference between an algebraic equation and an algebraic inequality?

Dec 19, 2014

An equation
The word says it all: equal.
In an equation, the left and right part are equal to each other. you might have the equation:
$2 x + 5 = 3 x - 7$
There is an $x$ for which this is true. By solving this equation, you can find it. (see this as a challenge)

An inequality
The word says it all: inequal => NOT equal.
In an inequality, there are other symbols between the left and the right part. These symbols don't signify equality, but inequality. You have symbols like:

• Greater than $>$
• Smaller than $<$
• Greater than or equal to $\ge$
• Smaller than or equal to $\le$

There usage is just as you might expect from their English meanings.
$2 x + 5 \le 3 x - 7$
Means that there is an $x$ for which it is true, that $2 x + 5$ is less than or equal to $3 x - 7$. (See this as a challenge as well)