Download Notes 3.1

Section 3.1
Solving One-Step Equations
Vocabulary:
two operations that undo each other
Inverse Operations:________________________________________________.
equations that have the same solutions
Equivalent Equations:______________________________________________.
isolate the variable on one side of the = sign
To solve an equation, you must _______________________________________.
Solving and equation using addition or subtraction
1. 𝑥 + 3 = 5
−3 −3
2. −7 + 𝑐 = −9
+7
+7
𝑥=2
𝑐 = −2
Always
circle your
final
answer
3. −11 = 𝑛 − (−2)
−2
−2
−13 = 𝑛
How can you check your answers
Substitute
the value back in for the variable
_______________________________________?
Does 𝑥 = −2 for the equation 14 = 12 − (𝑥)? Why
14 = 12 − (−2)
14 = 12 + 2
14 = 14
Match the real life problems with equation.
𝑥+7=9
𝑥−2=7
a. You have x dollars and
your friend repays you the
$7 he owes you. You now
have $9. How much did
you have originally?
b. A 9 foot post extends X
feet below the ground and
7 feet above the ground.
What is the length X buried
below the ground?
9-x=7
c. The temperature was X
F˚. What fell 2 F˚ and it
now 7 F˚. What was the
original temperature?
Geometry application: An equilateral triangle has a perimeter of
42 inches. Write and solve an equation to find the length of the
side of the triangle.
𝑠𝑜,
𝑋
𝑋
P=42
𝑋 + 𝑋 + 𝑋 = 42
3𝑋 = 42
3
3
𝑥 = 14
𝑋
The inverse operation of multiplication is ______________
division
The inverse operation of division is _________________
multiplication
18 = −2𝑎
−2
−2
−9 = 𝑎
𝑚
3
−4 •
= − • −4
−4
4
𝑚=
12
4
𝑚=3
30𝑏 = 5
30 30
1
b=
6
4
−5
−5
• − 𝑥 = 72 •
5
4
4
18
72 −5
𝑥=
•
1
4 1
𝑥 = −90
2•
𝑧
= −5 • 2
2
𝑧 = −10
2
17
3 11
3
𝑦
=
5
• 3 y= 3 •
3
1
1
𝑦=
17 3
•
3 1
𝑦 = 17
Write and solve an equation to answer the question.
Each household in the United States receives about 676
pieces of junk mail per year. About how many pieces does a
household receive per week?
52𝑥 = 676
Each household receives
about 13 pieces of junk mail
per week
𝑥 = 13
You ate three of the eight pizza slices and you paid $3.30 as
your share of the cost. How much did the whole pizza cost?
8 3
8
• 𝑝 = $3.30 •
3 8
3
𝑝=
3.30 8
•
1
3
𝑝=
26.40
3
= 8.80
The whole pizza cost $8.80
Hint: 52 weeks
per year