# Solving linear equations by factoring

I usually teach solving linear equations by balancing both sides e.g.

$$\begin{array}{cccc} 2x&+&3&=&5\\ &&\color{red}{-3}&&\color{red}{-3}\\ 2x&&&=&2\\ \color{red}{\div2}&&&&\color{red}{\div2}\\x&&&=&1 \end{array}$$

Recently I have been considering teaching students to solve via factoring $$\begin{array}{cccc} 2x&+&3&=&5\\ &&\color{red}{-5}&&\color{red}{-5}\\ 2x&-&2&=&0\\ 2(x&-&1)&=&0\\x&&&=&1 \end{array}$$

I think an advantage might be that solving quadratic equations is more aligned with previous learning. However I can see students being confused by factoring.

Has anybody taught solving linear equations by factoring? What were the outcomes for the students and future progress?

Any thoughts would be appreciated.

• I have no answer because I would never have thought to do this, but that makes me even more interested in seeing answers here. Is this effective? How and why? May 3, 2015 at 2:11
• Perhaps I'm too detached from a learner's way of thinking, but is there really a difference for them? There hardly is any for me. May 3, 2015 at 12:06
• @gitgud in my experience they are very different for students. Different still is using inverse functions $5\implies -3\implies \div2 \implies 1$ they tend to find this easiest to understand. (Ed: fixed MJ, it is hoped, quid)
– Karl
May 3, 2015 at 12:50
• To clarify the last step is the zero factor property not division by 2
– Karl
May 3, 2015 at 12:59
• Absolutely, to students there would be a huge difference between the two methods. My authority comes from working with tons of high school and early college students. The important criterion will be long term progress. May 9, 2015 at 8:25