1. 2-5 Solving Equations with the Variable on Each Side

2. 4 Steps for Solving an Equation
1) Simplify each side of the equation.
2) Get the variables together first.
3) Get the lone numbers together.
4) Get the variable by itself.

3. Solve: 3x – 7 = 2x + 5 3x – 7 = 2x + 5 x – 7 = 5 Simplify
-2x -2x Subtract 2x from both sides to combine the x’s on one side.
x – 7 = 5 Simplify
Add 7 to both sides to get x by itself.
x = 12 Simplify
Check: 3(12) – 7 = 2 (12) + 5
36 – 7 =
29 = 29 TRUE

4. Solve: 4a + 3 = 3a + 5
4a + 3 = 3a + 5
-3a -3a Subtract 3a from both sides
a + 3 = 5 Simplify
Subtract 3 from both sides
a = 2 Simplify
Check: 4(2) + 3 = 3(2) + 5
8 + 3 = 6 + 5
11 = 11 TRUE

5. Solve the following equation.
6x + 5 = 7x – 3
Answer: x = 8

6. Solve equations with Grouping Symbols
4(2r – 8) = 1/7 (49r + 70)
8r – 32 = 7r + 10 Use Distributive Property
-7r -7r Subtract 7r from both sides
r – 32 = 10 Simplify
Add 32 to both sides
r = 42 Simplify
Check: 4(2(42) – 8) = 1/7(49(42) + 70)
4(84 – 8) = 1/7( )
4(76) = 1/7(2128)
304 = TRUE

7. Identity: Equations that are true for all values of the variables.
Solve: 4(t + 20) = 1/5(20t + 400)
4t + 80 = 4t Distribute
-4t t Subtract 4t
80 = Simplify
Does 80 equal 80?? TRUE and the equation is an IDENTITY.
Therefore, the answer is ALL NUMBERS

8. No Solution Equations Solve: 8(5c – 2) = 10(32 + 4c)
40c – 16 = c Distribute
-40c c Subtract 40c
-16 = Simplify
Does -16 equal 320?? FALSE
Therefore the answer is NO SOLUTION!!

9. Check Your Progress #4
A purse is on sale for one fourth off the original price, or $12 off. What was the original price of the purse?
A. $12 B. $36 C.$48 D. $60
1/4x = 12
x = 48
Answer: C. $48

10. Homework #14
p even, 49-50