# What is x if 3x 3x 6

## Solving equations through equivalence transformations

bettermarks »Math book» Algebra and functions »Linear equations and inequalities» Setting up, solving and applying equations »Solving equations through equivalence transformations

Here you will learn how you can systematically solve equations with the help of equivalent transformations and how you can check whether the solution is correct.

### equivalent equations

Two equations are when they have the same.

The equations 3x + 7 = 16 and x = 3 are equivalent, because both equations have the solution set L = {3}.

The equations 3x + 7 = 16 and 3x + 6 = 15 are equivalent because both equations have the solution set L = {3}.

The equations 3x + 7 = 16 and 3x + 6 = 16 are not equivalent, because the solution sets are different: = {3} and = {}.

### Special amounts of solution

Is an equation always solvable "Does an equation only ever have one solution? A linear equation has in a given basic set either ... - no solution (then it is not solvable), - one solution or - infinitely many solutions.

Solve the equation in the basic set ℕ.

Transform the equation equivalently

Solve the equation in the basic set ℤ.

Transform the equation equivalently

Solve the equation in the basic set ℕ.

Transform the equation equivalently

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