# Solving One-Step Linear Equations with Fractions

Some linear equations can be solved with a single operation. For this type of equation, use the inverse operation to solve. The easiest type involves only an addition or a subtraction.

Example 1:

Solve.

$a+\frac{1}{7}=\frac{3}{7}$

The inverse operation of addition is subtraction. So, subtract $\frac{1}{7}$ from both sides.

$a+\frac{1}{7}-\frac{1}{7}=\frac{3}{7}-\frac{1}{7}$

Simplify.

$a=\frac{2}{7}$

Also, we can solve linear equations when only multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of $1$ .

Example 2:

Solve.

$\frac{y}{4}=300$

The inverse operation of division is multiplication. So, multiply both sides by $4$ .

$\frac{y}{4}\cdot 4=300\cdot 4$

Simplify.

$y=1200$

Example 3:

Solve.

$26=-\frac{13}{6}x$

To isolate the variable $x$ (to get a coefficient of $1$ ), multiply both sides by $-\frac{6}{13}$ which is the reciprocal of $-\frac{13}{6}$ .

$26\cdot \left(-\frac{6}{13}\right)=-\frac{13}{6}x\cdot \left(-\frac{6}{13}\right)$

Simplify.

$x=-12$