Here's a list of techniques useful for solving equations by turning them into equivalent equations:

- Simplify either side (or both);
- Add or subtract the same expression to both sides (and then simplify them);
- Multiply or divide both sides by the same nonzero constant (and then simplify them);
- Swap the sides.

A **linear equation**
is an equation whose sides are both linear expressions.
Linear equations in one variable can always be solved using this method:

- Simplify both sides (if necessary).
- If there is a variable term on the right-hand side, then subtract this term from both sides (and simplify them).
- If there is a constant term on the left-hand side, then subtract this term from both sides (and simplify them).
- If there is now a coefficient on the variable on the left-hand side, then divide both sides by that coefficient (and simplify them).

Inequalities are solved in the same way as equations, except for this important point:

- If you multiply or divide both sides by a negative number, then you must switch the direction of the inequality.

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