What does "equivalent form of the equation" mean?

The term "equivalent form of the equation" refers to a different expression of the same mathematical equation that while it may look different, has the same solution set as the original. In other words, equivalent equations have the same truth value for any variable that appears in the equation.

For an algebraic equation, equivalent forms can often be achieved by performing operations on both sides of the equation that do not change the solutions. These operations can include:

1. Adding or subtracting the same number or expression to both sides 2. Multiplying or dividing both sides by the same non-zero number or expression 3. Simplifying either side of the equation 4. Expanding or factoring expressions 5. Applying algebraic properties like distribution or combining like terms

For example, if you have a simple linear equation like: 2x + 3 = 7

Equivalent forms of this equation could include: 2x = 4, which is achieved by subtracting 3 from both sides, or x = 2, which is achieved by further dividing both sides by 2.

All of these forms are equivalent because they all have the same solution for x, which is x=2.