At some point a math student needs to move from learning algebra to doing algebra. Many techniques that students learn are designed to facilitate a person’s understanding and remembrance of algebraic processes and are not optimized for efficiency or speed. Adding a number to both sides of an equation or always using a least common denominator when adding fractional expressions are examples of the conflation of technique and reason for the technique combined into one rule.
But as students move into the next level math courses,precalculus and calculus, algebra becomes a just a tool for exploring new concepts. At this point a math learner should be thinking about the new ideas not algebraic processes. The second term of precalculus with its plethora of proportions, equations and identities is the place, I think, to make this jump. Therefore I will be modeling fast algebra techniques like those in the image below.
Fast Algebra Techniques
I have written about these matters before. See this post and this post and this post for other takes on fast algebra techniques.
Math Thoughts 
Dude .. Thanks a lot .. This has helped me .. As day after tomorrow I Am supposed attended my Maths Exam for 12 th Std. .. All I am poor in maths is Algebra .. This one went through my mind .. Thanks a lot .. I Appreciate
Amazing, but what is the official term for this technique?
You know like there are terms such as substituition and cross multiplication etc.
Thanks.
After much experience doing Algebra, these techniques come out. You will glean them after doing many many problems.
Thanks Helped Me Alot
Thank you so much I got it now:)
thanks for this site now I can solve algebra easiely
Good ideas! Simple and easy to explain
Is the very last one right?
Easy to understand and teach someone. Appreciate the hardwork
This technique is more good as opposed to this one
X+5=7
X+5-5=7-5
.
Trick to remember L.H.S to R.HS or RHS to LHS operations are changed .
+ to –
×to ÷
– to +
÷ to ×