Example 1
Solve 3x + 5 = 20.
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check: 3(5) + 5 = 20 ✓
Answer: x = 5
⚖️ Grade 7 · equations · session 5 of 12 · 60 minutes · ⭐ Plus
Solving equations px + q = r
An equation is a balance: both sides are equal. To find x, do the same thing to both sides, undoing operations in reverse order: first the + or −, then the × or ÷.
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
- The balance9 min
- Decimals and fractions9 min
- Word problems9 min
- Activity 17 min
- Activity 27 min
- Activity 35 min
- Quiz6 min
- Set the project4 min
By the end you can
- Solve px + q = r using inverse operations on both sides
- Solve equations with negative and decimal numbers
- Write and solve an equation from a word problem
- NJSLS-M 7.EE.B.4.a (Common Core 7.EE.4)
Before you start
- Combining like terms
- Operations with integers
Have ready
- The balance tool on screen
Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE
Warm-up · think first
I think of a number, multiply it by 3 and add 5. I get 20. What was my number?
Show the answer
Undo backwards: 20 − 5 = 15, then 15 ÷ 3 = 5. As an equation: 3x + 5 = 20, x = 5.
Teacher tip: Let pupils make up their own think-of-a-number puzzles.
Part 1 of 3 · learn, see, practise
The balance: same to both sides
An equation like 3x + 5 = 20 says both sides weigh the same.
Whatever you do to one side, do to the other: the balance stays level.
Undo in reverse: subtract 5 from both sides, then divide both sides by 3.
The equation balance
Purple bags are x; yellow squares are 1s. Take the same away from both sides, then share into equal groups.
- Solve 3x + 5 = 20 on the balance.
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
- 4
- -2
- -4
- -6
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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: Decimals and fractions, with practice at three levels
- Part 3: Word problems to equations, with practice at three levels
- Class activity 1: Balance puzzles
- Class activity 2: Arithmetic vs algebra
- Class activity 3: Make your own
- A 8-question quiz
- After-class project: Equation escape room
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Solving equations px + q = r: questions
How do you solve px + q = r?
Subtract (or add) q on both sides, then divide both sides by p. Check by substituting.
What is the difference between an arithmetic and an algebraic solution?
Arithmetic works backwards from the answer step by step; algebra writes an equation and solves it. They use the same operations in the same order.
Which standard is this?
New Jersey 7.EE.B.4.a (Common Core 7.EE.4a).
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