Multiplying (or dividing) the same non-zero number to both sides of an equation does not change its solution set.

**Example:**

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so if 6*x* = 12,
then 18*x* = 36 for the same value of *x* (which in this
case is *x* = 2).

The way we use the multiplication principle to solve equations is that it allows us to isolate the variable by getting rid of a factor that is multiplying the variable.

**Example:** 2*x* = 6

To get rid of the 2 that is
multiplying the *x*, we can divide both sides of the equation by 2, or
multiply by its reciprocal (one-half).

Either divide both sides by 2:

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or multiply both sides by a half:

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- Whether you prefer to think of it as dividing by the number or multiplying by its reciprocal is not important, although when the coefficient is a fraction it is easier to multiply by the reciprocal:

**Example:**
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Multiply both sides by the
reciprocal of the coefficient, or _{}

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