Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

What makes equations equivalent?

Two equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2x = 8 are equivalent equations, because when we solve each of them as follows, they have the same solution set. Subtract 2 from both sides.

What does it mean for expressions to be equivalent?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).