1. Algebra 1
Section 2.7

2. Variables on Both Sides
If you have an equation with variables on both sides of the equals sign, the Addition Property of Equality is used to move all the variables to one side of the equation.

3. Did you check your answer?
Example 1
Solve 2x + 5 = x – 2.
2x + 5 = x – 2
2x + 5 – x = x – 2 – x
x + 5 = -2
x = -7
Did you check your answer?

4. Can we do it differently?
Example 2
Solve 3(x – 4) = 4(x – 6).
3x – 12 = 4x – 24
3x – 12 – 3x = 4x – 24 – 3x
-12 = x – 24
12 = x
Can we do it differently?

5. Example 2 Solve 3(x – 4) = 4(x – 6). 3x – 12 = 4x – 24

6. Solving Multi-Step Equations
Simplify both sides by removing any parentheses and combining like terms.
Move the variable terms to the desired side of the equation.

7. Solving Multi-Step Equations
Undo the addition or subtraction of the constant term.
Undo the multiplication or division done to the variable.

8. Example 3 Solve 5x + 3x – 4 = x + 2. 8x – 4 = x + 26 7
x =

9. Example 4 Solve 3(4x – 5) + 2 = 2(6x + 3). 12x – 15 + 2 = 12x + 6
-13 = 6
No solution!

10. No Solution?
An equation can have no solution if there is no value of the variable that makes the equation true.

11. Example 5 Solve 8 – (x – 4) = -2(x – 6) + x. 8 – x + 4 = -2x + 12 + x
Solution: All real numbers!
This is called an identity.

12. Definition
An identity is an equation that is true regardless of the value of the variable.
The solution to any identity is listed as the set of real numbers.

13. Example 6 2x – 6 + 6 = 3x + 2 – 2 + x 2x = 4x 2x – 4x = 4x – 4x
Solve 2(x – 3) + 6 = 3x + 2 – (2 – x).
2x – = 3x + 2 – 2 + x
2x = 4x
2x – 4x = 4x – 4x
-2x = 0
x = 0

14. Homework: pp