Skill: Identify equations with no solution

To identify an equation with no solution, simplify it until the variable is eliminated.

• If you get a false statement, such as $3=-2$, there is no solution.
• This means no value of $x$ can make the original equation true.

Example:

$$4x+3=4x-2$$

Subtract $4x$ from both sides:

$$3=-2$$

The variable has disappeared, but the statement $3=-2$ is false. Therefore, the equation has no solution.

The two sides have the same $x$-term but different constants, so they can never be equal.