Multi-Step Equations

Objective: Explain multi-step equations, apply the stated method, and check its conditions.

For ax+b=d with a≠0, undo addition first and multiplication second. Each operation must act on both sides. More complicated equations may first require distribution and combining like terms. Substitute the final value into the original equation to verify it. Check the original equation, not only the final simplified line.

Objective: Explain variables on both sides, apply the stated method, and check its conditions.

Collect variable terms on one side and constants on the other using equal operations. A nonzero remaining coefficient gives one solution. If all variable terms cancel, a true constant equality gives infinitely many solutions and a false equality gives none. Variable cancellation can produce no solution or infinitely many solutions.