Cogito
Algebra 1 · Chapter 1 · Lesson 4
Variables on Both Sides
Gather the letters on one side and the numbers on the other.
11 problems · about 22 minutes · A-REI.B.3
What this lesson teaches
The student solves linear equations with the variable appearing on both sides.
- Move every x term to one side and every number to the other.
- Moving the smaller x term keeps the coefficient positive.
- Substituting the answer back is the only proof it is right.
Warm Up
Straightforward practice. Get the method working first.
4 problems9x + 2 = 4x + 22. What is x?
Answer 4
Why x = 4.
3x + 1 = x + 9. What is x?
Answer 4
Why Subtract x.
6x = 2x + 16. What is x?
Answer 4
Why Subtract 2x.
5x − 4 = 3x + 6. What is x?
Answer 5
Why Subtract 3x, add 4.
Build It Up
The same ideas with more to keep track of.
3 problems2x + 9 = 5x. What is x?
Answer 3
Why Subtract 2x.
7x + 2 = 4x + 20. What is x?
Answer 6
Why 3x = 18.
x + 12 = 4x. What is x?
Answer 4
Why 3x = 12.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsOrder the steps for solving 6x + 1 = 2x + 13.
Answer 1. Subtract 2x from both sides 2. Subtract 1 from both sides 3. Divide both sides by 4 4. Check by substituting
Why Letters first, then numbers, then divide.
8x − 5 = 3x + 15. What is x?
Answer 4
Why 5x = 20.
Both Sides: 4x + 2 = 2x + 10. What is x?
Answer 4
Why x = 4.
Two Gyms: Gym A costs 20 + 5m; gym B costs 35 + 2m. After how many months are they equal?
Answer 5
Why 5 months.