1. Objective: To solve equations where the variable is on both sides.
Ch 3.4
Objective:
To solve equations where the variable is on both sides.

2. Rules for Solving Equations
1) Goal: Isolate the variable on one side of the equation.
2) Use Inverse Properties to undo operations.
1) Distribute & Combine Like terms
2) Undo Addition/Subtraction
3) Undo Multiplication/Division
3) Always do the same thing to both sides of the equation.

3. Solve.
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

4. Solve.
1) 4(x - 2) - 2x = 5(x - 4)
4x x = 5x - 20
2x - 8 = 5x - 20
-2x x
-8 = 3x - 20
12 = 3x

5. 2) 3(x + 2) - (2x - 4) = - (4x + 5)
3x x + 4 = - 4x - 5
x + 10 = - 4x - 5
+ 4x x
5x + 10 = -5
5x = -15
x = 4

6. 3) 5(m - 4) = [2(m - 5) - 5m]
5m - 20 = [2m m]
5m - 20 = [-3m - 10]
5m - 20 = m + 40
5m - 20 = 12m + 50
-5m m
-20 = 7m + 50
-70 = 7m
x = -10

7. Some of these are TRICKY!
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

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

9. 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

10. Use a variable equation to solve.
4) Find a number that is 20 more than 4
times its opposite.
Let x = the number
-x = the opposite
x = 4(-x) + 20
x = -4x + 20
+4x +4x
5x = 20
x = 4