M3.8.6 For the adult
Solving equations in two steps
A balance is level. The left pan holds 3 bags of x stones and 5 loose stones. The right pan holds 20 loose stones. How many stones are in each bag?
What this chapter teaches
A two-step equation is solved by undoing the steps backwards: take away or add the loose number first, then divide or multiply. With brackets, expand first or divide by the outside number. With x on both sides, take the same number of x from both sides.
Three questions to ask
There is no one right wording. Listen for the idea.
- In 3x + 5 = 20, why do we take away 5 before we divide by 3?
- How can you solve 2(x + 3) = 14 in two different ways?
- How do you check that x = 4 is right for 5x − 2 = 3x + 6?
After the chapter, the learner can
- Solve 3x + 5 = 20
- Solve equations with brackets, like 2(x + 3) = 14
- Solve 5x − 2 = 3x + 6, with x on both sides
What they copy into their notebook
Undo the steps backwards. Take away the loose number first, then divide. Expand a bracket first, or divide by the number outside. Always put the answer back.