# Difference Between an Inequality & an Equation

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On the surface, equations and inequalities can seem as if they are the same thing. While they are very similar in principle and in many practices, such as the ability to add and subtract any integer and multiply positive integers, there are some major differences between the two.

## Direction

• For an equation, there is no direction, both sides of the equation are always equal. For an inequality, however, one side will always be greater or less than the other side. When you multiply or divide an inequality by a negative number, you need to change the direction of the sign. For example, if the inequality is -4x > 8, and you divide the equation bye -4 to solve it, it would be x < -2.

## Solution is a Range, Not an Absolute

• In an equation, the answer you arrive to will be an discrete value. For example, in the equation 4x = 8, the answer is x = 2. The answer is simply 2. In an inequality, the answer is not a discrete value, but a range. For example, in the inequality 4x > 8, the answer is x > 2. The answer is not 2, but rather any number greater than 2.

• In an equation, you will only have one answer, x = b. In an inequality, especially with absolute values, you can have multiple answers. For example, for the inequality |x| > 2, then the answer would be x > 2 or x < -2. Rather than the one answer, you have two that could be true, likewise, it could be a discrete range, such as a < x < b.

## References

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