Solving Equations with No and Infinite Solutions

An equation with no solution is one where no value of the variable can satisfy the equation. For example, $$2x + 3 = 2x + 5$$ has no solution because 3 cannot equal 5.

An equation with infinite solutions is one where any value of the variable satisfies the equation. For example, $$3(x + 2) = 3x + 6$$ has infinite solutions because both sides are equivalent for any value of x.

m = -4.

No solution.

Infinite solutions.

w = -3.

No solution.

It means the equation has infinite solutions, as it holds true for all values of the variable.

It means the equation has no solution, as there is no value of the variable that can make the equation true.

The first step is to isolate the variable on one side of the equation by performing inverse operations.