Skill: Solve one-step division equations

In an equation such as

$$\frac{x}{a}=b,$$

the variable $x$ is being divided by $a$. To undo division, use the inverse operation: multiply both sides by $a$. Because you do the same operation to both sides, the equation stays balanced.

Example: Solve

$$\frac{x}{4}=\frac{3}{2}$$

1. Multiply both sides by $4$:

$$4\left(\frac{x}{4}\right)=4\left(\frac{3}{2}\right)$$

2. Simplify. On the left, $4$ and $4$ cancel. On the right:

$$x=4\cdot\frac{3}{2}=6$$

3. Check the solution by substituting $6$ for $x$ in the original equation:

$$\frac{6}{4}=\frac{3}{2}$$

This is true, so the solution is

$$\boxed{x=6}$$

To solve a one-step division equation, multiply both sides by the nonzero number that divides the variable, then check your answer by substitution.