Students will practice solving certain multi-step equations mentally. Basically, my strategy is to reduce the number of terms and complexity of each term, for the sake of memory, until the answer becomes obvious. For example, here's how I would solve

$$7x - 3(2 - 5x) = 8x$$First, I notice \(7x\) and \(8x\) on opposite sides, so I immediately subtract \(7x\) from both sides. Now I'm thinking \(-3(2 - 5x) = x.\) I distribute to get \(-6 + 15x = x.\) Now I see \(x\) on both sides, so I subtract it. Now I'm thinking \(-6 + 14x = 0.\) Now I add \(6\) to both sides and divide both sides by \(14,\) in a single step. Now I'm thinking \(x = 6/14.\) I think, \(6/14 = (2 \cdot 3)/(2 \cdot 7) = 3/7.\) Thus, \(x = 3/7.\) Finally, challenge your students to solve this mentally: