1. Lesson 1.1
Objective: To solve equations using addition, subtraction, multiplication, and division
Vocab:
Inverse operations:
Are operations that undo each other such as addition and subtraction.
Isolating the Variable:
means to get the variable by itself.

2. EX: x + 5 = – 13
subtract 5 from both sides
– – 5
simplify
x = – 18
check
– = – 13
EX: – 6 = x – 9
add 9 to both sides
simplify
3 = x
check
– 6 = 3 – 9

3. subtract 7 from both sides – 7 – 7
EX: 7 – x = 42
subtract 7 from both sides
– – 7
– x = 35
we are solving for x not – x.
+x +x
add x to both sides
0 = 35 + x
subtract 35 from both sides
– –35
– 35 = x
check
7 – (– 35) =42
We could of solved – x = 35 by dividing both sides by –1

4. Properties of Equality
Multiplication property If a = b, then ac = bc
Division property If a = b, and c ≠ 0, then a ÷ c = b ÷ c
Divide both sides by – 5
EX: solve
– 5x = 30
– 5
– 5
A number divided by itself always equals 1
x = – 6
check
– 5 • – 6 = 30

5. Multiply both sides by – 4
EX: solve x
= 32
Multiply both sides by – 4
– 4 x
(– 4)
= 32
(– 4)
The -4’s cancel –4
x = – 128
– 128
check
= 32
– 4
EX: solve 2 3
6 = – — x
Multiply each side by – — 3 2 3 ?
Why
– —
The reciprocal of –2/3 is – 3/2 2 3 2 3 – x – • 6 = – • 2 3 2
Check: - 2/3• –9 = 6
– 9 = x

6. Practice: Solve each equation
1) –3x = 27
X = –9
– – 3 2)
X= 40 3)
X = 32