Example 1
Solve 5x + 3 = 2x + 12.
- Subtract 2x: 3x + 3 = 12.
- Subtract 3: 3x = 9.
- x = 3. Check: 18 = 18 ✓
Answer: x = 3
⚖️ Grade 7 · equations · session 8 of 12 · 60 minutes · ⭐ Plus
Variables on both sides: one, none or infinitely many solutions
When x appears on both sides, gather the x-terms on one side. Most equations end as x = a number (one solution), but some end as 5 = 5 (always true: infinitely many) or 3 = 7 (never true: no solution).
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
- Gather the x-terms9 min
- Brackets first9 min
- How many solutions?9 min
- Activity 17 min
- Activity 27 min
- Activity 35 min
- Quiz6 min
- Set the project4 min
By the end you can
- Solve equations with x on both sides, brackets and like terms
- Tell whether an equation has one, no or infinitely many solutions
- Make up equations of each type
- NJSLS-M 8.EE.C.7.a, 8.EE.C.7.b (Common Core 8.EE.7)
Before you start
- Solving p(x + q) = r
- Combining like terms
Have ready
- The balance tool on screen
Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE
Warm-up · think first
Is 2x + 4 = 2(x + 2) ever false?
Show the answer
No! Expand: 2x + 4 = 2x + 4. Both sides are always the same, so every number works.
Teacher tip: Try x = 0, 5 and −3 to test it.
Part 1 of 3 · learn, see, practise
Gather the x-terms
Subtract the smaller x-term from both sides so x is on one side only.
Then solve the two-step equation that is left.
5x + 3 = 2x + 12 → 3x + 3 = 12 → 3x = 9 → x = 3.
After taking 2x from both sides
5x + 3 = 2x + 12 becomes 3x + 3 = 12. Finish it on the balance.
- Solve 3x + 3 = 12.
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
- 3
- 4
- 6
⭐ 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: Brackets and like terms first, with practice at three levels
- Part 3: One, none or infinitely many, with practice at three levels
- Class activity 1: Solve them all
- Class activity 2: Sort the equations
- Class activity 3: Build your own
- A 8-question quiz
- After-class project: Equation sorting game
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Variables on both sides: one, none or infinitely many solutions: questions
How do you solve equations with variables on both sides?
Expand brackets, combine like terms, subtract the smaller x-term from both sides, then solve the two-step equation.
When does an equation have no solution?
When the x-terms cancel and the numbers left are different, such as 1 = 5.
Which standard is this?
New Jersey 8.EE.C.7.a and b (Common Core 8.EE.7), included as a stretch for Grade 7.
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