Lesson 1.1

Objective: To solve equations using addition, subtraction, multiplication, and division

Are operations that undo each other such as addition and subtraction.

Inverse operations:

Isolating the Variable:

Vocab:

means to get the variable by itself.

EX: x + 5 = – 13 subtract 5 from both sides – 5 – 5 simplify

x = – 18

EX: – 6 = x – 9

check

add 9 to both sides

+ 9 +9 simplify

3 = x check – 6 = 3 – 9

– 18 + 5 = – 13

EX: 7 – x = 42 subtract 7 from both sides– 7 – 7

– x = 35 we are solving for x not – x.

+x +x

0 = 35 + x subtract 35 from both sides– 35 –35

add x to both sides

– 35 = x check 7 – (– 35) =42

We could of solved – x = 35 by dividing both sides by –1

– 5x = 30 Divide both sides by – 5 – 5 – 5

x = – 6 check – 5 • – 6 = 30

EX: solve The -5’s cancel

Properties of Equality

Multiplication property If a = b, then ac = bc

Division property If a = b, and c ≠ 0, then a ÷ c = b ÷ c

EX: solve

x

= 32 – 4 Multiply both sides by – 4

(– 4) x –4

= 32 The -4’s cancel

x = – 128check – 128

– 4= 32

(– 4)

EX: solve

6 = – 2—3

x Multiply each side by – 3—2

Why 3– —2 ? The reciprocal of –2/3 is – 3/2

– 32 • 6 = – 2

3• – 3

2x

– 9 = x Check: - 2/3• –9 = 6

Practice: Solve each equation

1) –3x = 27

2) 104

x

3) 84

1x

– 3 – 3 X = –9

4104

4 x

X= 40

1

48

4

1

1

4 x X = 32