Transcript Lesson 1.1

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.
EX: x + 5 = – 13 subtract 5 from both sides
–5
– 5 simplify
x = – 18
check
– 18 + 5 = – 13
EX: – 6 = x – 9
+9
+9
3= x
add 9 to both sides
simplify
check
–6=3–9
EX: 7 – x = 42
–7
–7
– x = 35
+x
+x
0 = 35 + x
– 35 –35
– 35 = x
subtract 7 from both sides
we are solving for x not – x.
add x to both sides
subtract 35 from both sides
check
7 – (– 35) =42
We could of solved – x = 35 by dividing both sides by –1
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
– 5x = 30
–5 –5
x =–6
Divide both sides by – 5
The -5’s cancel
check
– 5 • – 6 = 30
EX:
x
= 32
Multiply both sides by – 4
solve – 4
(– 4) x = 32 (– 4)
The -4’s cancel
–4
x = – 128
check – 128 = 32
–4
EX: solve
3
2 x Multiply each side by – —
6 = –—
3
2
3
Why – —
2 ? The reciprocal of –2/3 is – 3/2
2
– 3 • 6 = –
3
2
–9=x
•– 3
2
x
Check: - 2/3• –9 = 6
Practice: Solve each equation
1) –3x = 27
–3
2)
–3
x
 10
4
x
4   10  4
4
3)
X = –9
X= 40
1
x 8
4
4 1
4
 x  8
1 4
1
X = 32