Learning goals: Teacher Facing Explain (orally and in writing) why performing certain operations on an equation may create equivalent equations but performing other operations may not. Understand that dividing by a variable is not used in solving equations because it can lead to equations that have fewer solutions than the original equation. Understand that equations that are not true for any value of the variable(s) do not have solutions. Full lesson plan (warm-up, activities, synthesis, cool-down prompt) from Alg1.2 Linear Equations, Inequalities, and Systems, Algebra 1.