One & Two
Step Equations
INTEGRATED MATHEMATICS
Vocabulary
• Equation: A statement that the values of
two mathematical expressions are equal
• Inverse Operations: Operations that undo
one another
Solving a One-Step Equation
1) Separate the Equation
2) ISOLATE THE VARIABLE:
• Should It Stay or Should It Go (Variables on
Left/Constants on Right)
Examples:
𝒙=𝟕
𝒚 = 𝟕𝟐
Property of Equality
You can add or subtract any number to
BOTH sides of an equation and the equation
will still hold true.
One-Step Equations with
Addition/Subtraction
Ex.1) x + 2 = 6
Ex.2) a – 4 = 2
One-Step Equations with
Addition/Subtraction
Ex.3) 19 = y + 7
Ex.4) z – 7 = 4
One-Step Equations with
Addition/Subtraction
Try These:
1) x + 4 = 10
3) 15 = 23 + r
2) y - 2 = 12
4) -13 + z = 2
Property of Equality
You can multiply or divide BOTH
sides of an equation by any number
and the equation will still hold true.
An Easy Example: (don’t copy)
We all know that 3 = 3.
•
Would you ever put
deodorant under just one
arm?
But 3(4) = 3(4).
•
Would you ever put nail
polish on just one hand?
The equation is still true if
we multiply both sides
by 4.
•
Would you ever wear just
one sock?
Does 3(4) = 3? NO!
One-Step Equations with
Multiplication/Division
Ex.5) -2x = 8
Ex.6) 3y = 15
One-Step Equations with
Multiplication/Division
𝑦
𝑧
Ex.8) = 4
Ex.7) = 5
4
3
What Do We Do with Negative Fractions?
Recall that
𝑥 −𝑥
𝑥
− =
=
5
5
−5
−𝑥
=3 .
Solve
5
Multiply both sides
by -5.
 The
two negatives will
cancel each other
out.
 The two fives will
cancel each other
out.
One-Step Equations with
Multiplication/Division
Try These:
1) 25 = 5x
2) -4x = -12
𝑥
5
3) = 4
𝑧
2
4) - = 24
Two-Step Equations
1) Separate the Equation
2) Should It Stay or Should It Go
• Addition/Subtraction
• Multiplication/Division
3) Solve for Variable
Two-Step Equations
Ex.9) Solve 5x + 7 = 3
Two-Step Equations
𝑡
3
Ex.10) Solve + 15 = 45
Two-Step Equations
Ex.11) Solve 4 = -6y - 20
Two-Step Equations
Ex.12) Solve 11z + 8 = 30
Two-Step Equations
Ex.13) Solve 4 = -11 +
𝑝
−5
Two-Step Equations
1
7
Ex.14) Solve 20 – c = -9
Two-Step Equations
Try These:
1) 11x + 2 = 35
2) 8 = - 22 + 2b
3) 2 = 5x – 8
4) -32 = 4t - 16
5)
𝟒𝒏
𝟓
– 7 = –4
Write Linear Equations - ADDITION
The SUM of a number and 4
5 MORE than a number
2 PLUS 7
13 ADDED TO a number
A number INCREASED by 9
The SUM of two numbers
Write Linear Equations - Subtraction
3 LESS THAN a number
A number DECREASED BY 15
7 MINUS a number
A number Subtracted from 6
The DIFFERENCE BETWEEN two numbers
Write Linear Equations - Multiplication
8 TIMES a number
A number MULTIPLIED BY 9
TWICE a number
𝟑
𝟒
𝑶𝑭 a number
The PRODUCT of two numbers
Write Linear Equations - Division
The QUOTIENT of 6 and a
number
A number DIVIDED by 4
The RATIO of 7 and a
number