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Solve one-step multiplication equations

A one-step multiplication equation has the form ax=bax=b or xa=bxa=b, where a known rational coefficient multiplies an unknown; solving means identifying division by that coefficient as the inverse operation and determining the value that makes both sides equal. The reasoning applies to positive and negative integers, fractions, and terminating decimals, includes checking by substitution, and distinguishes the coefficient from the unknown rather than treating multiplication as addition.

Detailed Explanation: Solve one-step multiplication equations

A one-step multiplication equation has a number multiplying the unknown, such as

ax=b.ax=b.

To isolate the unknown, use the inverse of multiplication: divide both sides by the coefficient.

Example

Solve:

−34x=6-\frac{3}{4}x=6

  1. Identify the coefficient of xx.

    The coefficient is −34-\frac{3}{4}.

  2. Divide both sides by −34-\frac{3}{4}:

x=6−34x=\frac{6}{-\frac{3}{4}}

  1. Dividing by a fraction is the same as multiplying by its reciprocal:

x=6(−43)=−8x=6\left(-\frac{4}{3}\right)=-8

  1. Check the answer by substituting −8-8 for xx:

−34(−8)=6-\frac{3}{4}(-8)=6

Since the left side equals the right side, the solution is

x=−8\boxed{x=-8}

Remember: divide by the coefficient, not by the unknown.

Learn by doing: Solve one-step multiplication equations

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