1. Objective - To solve equations with the variable in both sides.
2x + 4 = 5x - 17
2x + 4 = 5x - 17
2x + 4 = 5x - 17
-2x x
-5x x
4 = 3x - 17
-3x + 4 = -17
21 = 3x
-3x = -21
7 = x
x = 7

2. Rules for Solving Equations
1) Goal: Isolate the variable on one side of the equation.
2) Undo operations with their opposite operation.
3) Always do the same thing to both sides of the equation.
4) Easiest to undo add/subtract
before multiply/divide.

3. Solve.
1) 4(x - 2) - 2x = 5(x - 3)
4x x = 5x - 15
2x - 8 = 5x - 15
-2x x
-8 = 3x - 15
7 = 3x

4. 2) 3(x + 2) - (2x - 4) = - (4x + 1)
3x x + 4 = - 4x - 1
x + 10 = - 4x - 1
+ 4x x
5x + 10 = -1
5x = -11
x = =

5. 3) 5(m - 6) = [2(m - 7) - 5m]
5m - 30 = [2m m]
5m - 30 = [-3m - 14]
5m - 30 = m + 56
5m - 30 = 12m + 66
-5m m
-30 = 7m + 66
-96 = 7m

6. Solve each equation below.
a) 3x - 5 = 2x + 12
b) 3x + 8 = 2(x + 4) + x
-2x x
3x + 8 = 2x x
x - 5 = 12
3x + 8 = 3x + 8
-3x x
x = 17
8 = 8
True !
One Solution
Identity
x = any real number
c) 3x + 2 = 2(x - 1) + x
3x + 2 = 2x x
3x + 2 = 3x - 2
-3x x
2 = -2
False !
No Solution

7. Solve. 4) 4(y - 2) + 6y = 7(y - 8) - 3(10 - y)
-8 = -86
False Statement
No Solution

8. 5) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19)
Solve.
5) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19)
12 + 3k - 6k - 8 = 5k k + 19
-3k + 4 = -3k + 4
+3k k
4 = 4
True Statement
Infinitely Many Solutions
x = any real number