Download Two Step Equation Notes

Two-Step Equations B
Tool Box:
1.
2.
3.
Summary:
Inverse
Operations
Properties of
Equality
Like Terms
Question:
Two-Step Equations contain “two”
operations
To solve two-step equations, use
inverse operations to “undo” each
operation in reverse order
EXAMPLE: 𝟓𝒙 − 𝟐 = 𝟏𝟑
𝟓𝒙 − 𝟐 = 𝟏𝟑
1.Write the equation
2. Draw railroad tracks
3. Isolate the variable
4. Addition Property of Equality
(add 2 to both sides of the equation)
𝟓𝒙 − 𝟐 = 𝟏𝟑
𝟓𝒙 − 𝟐 = 13
+2
+ 2
𝟓𝒙
= 𝟏𝟓
5𝑥
=
5
𝟖 =
𝟖 =
-15
-7 =
( - 3) -7 =
21
15
𝟖 =
EXAMPLE:
𝒄
+
−𝟑
𝒄
+
-
−𝟑
5. Simplify/Combine Like Terms
6. Division Property of Equality
(Divide both sides of the equation
by 5)
7. Simplify
5
𝒄
−𝟑
+
𝟏𝟓
𝟏𝟓
𝟏𝟓
15
𝒄
−𝟑
𝒄
−𝟑
(-3)
= c
1 Write the equation
2 Draw railroad tracks
3 Isolate the variable
4 Subtraction Property of Equality
(subtract 15 from both sides of the
equation)
5 Combine Like Terms/Simplify
6 Multiplication Property of
Equality
(multiply both sides of the equation
by -3)
7 Simplify
Solve by Combining Like Terms
EXAMPLE:
𝟒𝒂 + 𝟑𝒂 = 𝟔𝟑
𝟒𝒂 + 𝟑𝒂 = 𝟔𝟑
1. Write the equation
2. Draw railroad tracks
𝟕𝒂
= 𝟔𝟑
𝟕𝒂
𝟔𝟑
=
𝟕
a
3. Combine Like Terms (4a+ 3a)
4. Isolate the variable
5. Division Property of Equality
(Divide both sides of the equation
by 7)
6. Simplify
𝟕
=
9
Equations with Negative Coefficients
4
Example:
𝟒 −
𝒙
−
𝑥
=
𝟏𝟎
𝟒 − 𝟏𝒙 =
𝟒 + (−𝟏𝒙) =
-4
𝟏𝟎
𝟏𝟎
- 4
- 1x =
−𝟏𝒙
=
−𝟏
x
=
=
10
1. Write the equation
2. Train Tracks
3. Identity Prop. x = -1x
4. Subtraction Property
5. Subtraction Property of Equality
(Subtract 4 from both sides of the
equation
6. Simplify/Combine Like Terms
7. Division Property of Equality
(Divide both side of the equation by
–1)
8. Simplify
6
𝟔
−𝟏
-6
Combine Like Terms Before Solving
𝑚 − 5𝑚 + 3 = 47
Example:
𝑚 − 5𝑚 + 3 = 47
𝟏𝑚 − 5𝑚 + 3 = 47
− 𝟒𝒎 + 𝟑 = 𝟒𝟕
- 3
- 4m
−𝟒𝒎
−𝟒
- 3
= 44
=
m
=
Try It!
1.
2.
3.
37 = 4d + 5
8y + 6 – 9y = -4
𝑘
5
See Next Page
− 10 = 3
𝟒𝟒
−𝟒
-11
1. Write the equation
2. Train Tracks
3. Identity Property m = 1m
4. Combine Like Terms 1m and 5m
5. Subtraction Property of Equality
(Subtract 3 from each side of the
equation)
6. Simplify/Combine Like Terms
7. Division Property of Equality
(Divide both sides of the equation
by – 4)
8. Simplify
FUNCTIONS
y is a function of x or y depends on x
y = 3x
- 15
Dependent variable
Independent Variable
Range
Domain
Output
Input
EXAMPLE: The output of a function is 2 more
than 4 times the input. Find the input when the
output is 14.
Output is 2 more than
“y”
= “2 + “
14
=
2
+
4x
Solve the equation
14 = 4x +
2
14
-2
=
4x
12
12
4
=
=
4x
4𝑥
4
3
=
x
+
-
4 times input
“4x”
2
2
TRY IT!!
The output of a function is 3 less than 6 times the
input. Find the input when the output is 15
Write an equation for the function.
Let
y be the output and x be the input
“Is” means equal to, “more than”
means to add, “times” means to
multiply
Substitute “14” in for the output
“y”
1 Write the equation
2 Draw the railroad track
3 Isolate the variable
4 Subtraction Property of Equality
(subtract 2 from each side of the
equation
5 Combine Like Terms/Simplify
6. Division Property of Equality
(divide both sides of the equation
by 4)
7 Simiplify