Equations can be solved in many ways. In this lesson, we focused on equations with a specific structure, and two specific ways to solve them. 

Suppose we are trying to solve the equation $\frac45(x+27)=16$. Two useful approaches are:

• Divide each side by $\frac45$.
• Apply the distributive property.

In order to decide which approach is better, we can look at the numbers and think about which would be easier to compute. We notice that $\frac45 \boldcdot 27$ will be hard, because 27 isn't divisible by 5.  So, distributing the $\frac45$ is not the best method. But $16 \div \frac45$ gives us $16 \boldcdot \frac54$, and 16 is divisible by 4. So, dividing each side by $\frac45$ is a good choice.

$\begin{aligned} \tfrac45 (x+27) &= 16 \\ \tfrac54 \boldcdot \tfrac45 (x+27) &= 16 \boldcdot \tfrac54 \\ x+27 &= 20 \\ x &= \text- 7 \\ \end{aligned}$

Sometimes the calculations are simpler if we first use the distributive property. Let's look at the equation $100(x+0.06)=21$. If we first divide each side by 100, we get $\frac{21}{100}$  or 0.21 on the right side of the equation. But if we use the distributive property first, we get an equation that only contains whole numbers. 

$\begin{aligned} 100(x+0.06) &= 21 \\ 100x+6 &= 21 \\ 100x &= 15 \\ x &= \tfrac{15}{100} \\ \end{aligned}$