Cogito
Integrated Math 1 · Chapter 1 · Lesson 1
Solving Linear Equations
Undo the operations, one at a time.
12 problems · about 20 minutes · A-REI.B.3, A-REI.A.1
What this lesson teaches
The student solves multi-step linear equations and justifies each step.
- An equation is a balance; do the same to both sides.
- Undo operations in the reverse of the order they were applied.
- Vanishing variables leave either every solution or none.
Warm Up
Straightforward practice. Get the method working first.
5 problems4x + 6 = 26. What is x?
Answer 5
Why 5.
The variables cancel and leave 7 = 7. How many solutions?
Answer Every number is a solution.
Why A true statement means every value works.
x + 9 = 15. What is x?
Answer 6
Why Subtract 9.
4x = 28. What is x?
Answer 7
Why Divide by 4.
5x − 3 = 22. What is x?
Answer 5
Why Add 3, then divide by 5.
Build It Up
The same ideas with more to keep track of.
3 problems3(x + 2) = 18. What is x?
Answer 4
Why Divide by 3 first.
7x = 4x + 12. What is x?
Answer 4
Why Subtract 4x from both sides.
2x + 3 = 2x + 9. How many solutions?
Answer 0
Why The variables cancel, leaving a false statement.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut the solving steps for 3x + 5 = 20 in order.
Answer 1. Subtract 5 from both sides. 2. Simplify to 3x = 15. 3. Divide both sides by 3. 4. Check by substituting back.
Why Addition is undone before multiplication.
6x − 4 = 2x + 12. What is x?
Answer 4
Why Collect to 4x = 16.
The Equation: 2x + 7 = 19. What is x?
Answer 6
Why 6.
The Tickets: Tickets cost $8 each plus a $5 booking fee. A total of $53 buys how many tickets?
Answer 6
Why 6 tickets.