The single most powerful technique for helping my students understand how to solve equations in which the variable appears exactly once is what I call the "order of operations ladder." The ladder lists operations to the variable on the left, in the order they are performed according to the order of operations, and the inverse operations on the right.
I wrote this worksheet for my struggling Algebra 2 students: they simply had no idea how to solve equations, so I had to go back and reteach this to them.
(Explaining this in text might not be the most effective way to go... Hover over thumbnail image 3 right now, and you'll see what I'm calling an order of operations ladder looks like!)
------ hover over thumbnail image 3 --------
For instance, if a student were to solve the equation (3x + 4)/11 =2,
the ladder would list the operation "multiply by 3", "add 4", and "divide by 11" on the left side, and then starting from the bottom of the right side, the list would have the inverse operations "multiply by 11," "subtract 4," and "divide by 3," which are the exact steps required to solve this sort of linear equation in which the variable appears exactly once.
For students to use the ladder, they must simply "climb up" the right side of the ladder, performing those operations in order.
While my students initially resist this approach, they find it invaluable when solving literal equations, and it also comes in handy when they need to do inverse functions later on.
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.