Equations are equivalent if values for the variables that make one equation true also make the other equation true. One way to create equivalent equations is to correctly use valid moves.

Valid moves include:

• Using the distributive property. ($2(x+6)$ is equivalent to $2x + 12$)
• Combining like terms.  ($2x + 1 - x + 5$ is equivalent to $x + 6$)
• Adding the same value to each side.
• Subtracting the same value from each side.
• Multiplying each side by the same non-zero value.
• Dividing each side by the same non-zero value.

For example, all of these equations are equivalent:

For these equations, the valid moves are used correctly, so all of the equations are equivalent. The last equation shows that 3 is the value for $x$ that makes the equation true. Because all of the equations are equivalent, 3 is the value for $x$ that makes each of these equations true.