Skill: Solve one-step multiplication equations

Explanation and Free Practice Resources

A learner understands that a one-step multiplication equation represents a product relationship, such as $ax=b$ , and solves for the unknown factor by applying the inverse operation: dividing both sides by the nonzero coefficient. The reasoning preserves equality, applies to positive and negative integers and commonly used rational numbers, and includes checking the solution by substitution; multi-step, variable-on-both-sides, and nonlinear equations are beyond this scope.

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Detailed Explanation: Solve one-step multiplication equations

A one-step multiplication equation has the form

ax=b

where $a$ is the coefficient multiplying the unknown $x$ . To find $x$ , use the inverse operation of multiplication: divide both sides by $a$ . Dividing both sides keeps the equation balanced.

Example: Solve $-3x=12$ .

The coefficient of $x$ is $-3$ . Divide both sides by $-3$ :

\frac{-3x}{-3}=\frac{12}{-3}

Simplify both sides:

x=-4

Check the solution by substituting $-4$ for $x$ in the original equation:

-3(-4)=12

Since $12=12$ , the solution is correct.

Therefore,

\boxed{x=-4}

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One-Step Equation - Multiplication/Division - Solve

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