Solving 2 Step Algebraic Equations

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SWBAT solve 2 step algebraic equations.

Big Idea

Students use order of operations in reverse to solve equations.

Do Now

10 minutes

For the Do Now problems, students' understanding of solving one step equations will be assessed.  I want to clarify any questions or misconceptions before continuing on to two step equations.

Do Now

Solve each equation and check.

1)  a + 2.8 = 7

2)  x / 4 = 12



Mini Lesson

15 minutes

For solving two step equations, students will continue to use inverse operations.  However, to make this strategy more relatable, I will refer to it as the Sock and Shoe Method.

I will share with students the idea behind the Sock and Shoe Method.

Everyday you get dressed for school.  There is a certain order that you put on your uniform.  And you always put on your socks before your shoes.  When we're solving equations we are undoing operations or undressing them.  We will work backwards.  This means that we will undo the addition and subtraction first and then the multiplication and division. We will perform the order of operations in the reverse order.

For the first example I will use algebra tiles and the Solving Algebraic Equations with Algebra Tiles Worksheet, page 1.  Students used these in the previous lesson, Solving 1 Step Equations.


Example 1 - Solve the equation algebraically.    2b + 2 = 8

What tiles do we need to represent this equation?

Students should use 2 green rectangles, and 10 yellow circles.  They should set up the equation on the worksheet using the tiles.

What operations have been done to the variable?

Students should identify that the equation involves addition and multiplication.

If we are "undressing" the equation, what should we undo first?

We will undo the addition first. Students should remove 2 yellow tiles from the left side and 2 yellow tiles from the right side.

What operation do we have left and how are we going to undo it using the tiles?

Students should recognize that we have multiplication left and we need to divide both sides in half.

For the next few examples, I will lead students through the process of using inverse operations.  I will ask the following questions for each problem:

What operations have been done to the variable?

What should we undo first? 

What is the inverse operation?

Example 2 - Solve the equation algebraically.  6 = 3 + 3x

Example 3 - Solve the equation algebraically.   3x + 2 = 17

Example 3 - Solve the equation algebraically.   1/3a + 6 = 8


Group Work

15 minutes

I will assign students two step equations to solve.  I will encourage students to discuss their strategy, work and answers with their group.

Group Work

1)  2x + 7 = 21 

2)  6x - 12 = 12 

3)  x/4 + 2 = 10 

4)  x/3 - 5 = 8

 After 10 minutes, I will assign each group a problem to present to the class on a white board.  They must show their steps and explain their strategy.  To help with their presentation of the problem, I will remind students of the three questions they answered for the examples.

 What operations have been done to the variable?

What should we undo first? 

What is the inverse operation?

Lesson Summary

5 minutes

If students have shown an understanding of solving two step equations, I will present them with a challenge problem.  The challenge problem is an incorporation of applying the distributive property, combining like terms, and solving an algebraic equation.  Although this is a multi step problem, students have the skills to solve the equation.


2(x – 1) + 3(x + 7) = 4


If students have shown that there is not a thorough understanding of the concept, we will work through another problem together.

4x – 3 = 41