Today is rung 6 of 12 on this topic
Multi-step equations and inequalities
Can do: Solves equations with brackets and variables on both sides, and inequalities including the flip rule.
Why it matters
It's the algebraic engine for everything after. The inequality sign flip is the single most-forgotten rule in middle school.
What it looks like when it's wobbly
Forgets to flip the inequality when multiplying or dividing by a negative, and mishandles brackets.
⏱️ Two-minute check
"Solve 3(x − 2) = 2x + 5. Then solve −2x > 8."
Solid looks like: x = 11, and x < −4 with the flip.
The full activity for this topic · 20 minutes
Substitute Back Every Time
- 1Solve the equation showing every step with the operation written to the side.
- 2Substitute the answer back into the original. Non-negotiable.
- 3For inequalities, test a number from the solution set on the original — that's how they catch a missing flip themselves.
- 4Graph the solution on a number line with the right open or closed circle.
- 5Write a real situation the inequality could describe.
If it's too hard
Two-step equations, no brackets.
If it's too easy
Inequalities with variables on both sides, and compound inequalities.
Say this
"Test a number from your answer in the original. If it doesn't work, you missed the flip."