Example 1
Solve 3(x + 4) = 27.
- Divide both sides by 3: x + 4 = 9.
- Subtract 4: x = 5.
- Check: 3(5 + 4) = 27 ✓
Answer: x = 5
⚖️ Grade 7 · equations · session 6 of 12 · 60 minutes · ⭐ Plus
Solving p(x + q) = r: two ways
Equations with brackets, like 3(x + 4) = 27, can be solved two ways: divide both sides by 3 first, or expand the bracket first. Both reach the same answer; choose the quicker one.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up4 min
- Divide first9 min
- Expand first9 min
- Stories with brackets9 min
- Activity 17 min
- Activity 27 min
- Activity 35 min
- Quiz6 min
- Set the project4 min
By the end you can
- Solve p(x + q) = r by dividing first
- Solve by expanding first, and compare the two ways
- Write p(x + q) = r equations from word problems
- NJSLS-M 7.EE.B.4.a (Common Core 7.EE.4)
Before you start
- Solving equations px + q = r
- The distributive property
Have ready
- The balance tool on screen
Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE
Warm-up · think first
Three friends each add ₹4 to the same pocket money and get ₹27 in total. How much pocket money did each have?
Show the answer
27 ÷ 3 = 9 each, then 9 − 4 = 5. As an equation: 3(x + 4) = 27, x = 5.
Teacher tip: Ask whether anyone expanded instead.
Part 1 of 3 · learn, see, practise
Divide first
In p(x + q) = r, the bracket is multiplied by p. Undo that first: divide both sides by p.
Then undo the + q.
This is quickest when r divides exactly by p.
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Answers (for the teacher)
- 4
- 5
- -4
- -3
- 2
⭐ Part of Pure Faith Plus
The rest of this lesson is in Plus
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You have seen the plan, the warm-up and part 1. With Plus you also get:
- Part 2: Expand first, with practice at three levels
- Part 3: Stories with brackets, with practice at three levels
- Class activity 1: Two ways race
- Class activity 2: Which is quicker?
- Class activity 3: Area and perimeter
- A 8-question quiz
- After-class project: Two-method poster
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Solving p(x + q) = r: two ways: questions
How do you solve p(x + q) = r?
Divide both sides by p, then subtract q; or expand the bracket and solve px + pq = r.
Which method is better?
Dividing first is quicker when r divides exactly by p; expanding first is often easier with fractions or decimals.
Which standard is this?
New Jersey 7.EE.B.4.a (Common Core 7.EE.4a).
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