Algebra I Guided Notes: Solving Equations and Inequalities with Variables on Both
Sides
Lesson 2.4/3.4
Objective:
to solve equations and inequalities with variables on both sides
If there is a variable on both sides of the equation/inequality, (ISOLATE THE VARIABLE!)
1.
2.
3.
4.
5.
Distribute, combine like terms on each individual side.
Add or subtract to move the variable to the one side.
Add or subtract to move the constants to the other side.
Solve the equation/inequality.
**Remember with inequalities to switch the inequality sign if multiplying or dividing
both sides by a negative.
Examples
1)
6x + 3 = 4x + 9
2)
- 5 + 3x = 5 + 2 x
3)
x + 13 = 6 x - 2
4)
4(x + 1) = 2 x - 2
5)
- 2(3z - 4) = 10 - 6 z
6)
- 2(3z - 4) = 8 - 6 z
Special Case: No Solution:
true.
3x – 2 = 6 + 3x
no value of the variable can make the equation
Special Case: Identity:
3x + 6 = 6 + 3x
true for every possible value of the variable
7)
3x + 7 > x – 5
8)
9)
8x – 7 + 2x < 4x + 11
10)
3(x – 5) > 6x + 9
3(x – 4) > 3x + 7