Lesson 4.2
Rational Numbers & Equations
Solving One-Step Equations
Warm-Up
Evaluate each expression for the given value(s).
1. 3x – 2 when x = 5
13
2. 7 – 6y when y = –2
19
p
3.
– 12 when p = 10
2
–7
1
4.
d + (–2) when d = 12
4
5. 9m + 3n when m = –1 and n = 2
1
–3
Lesson 4.2
Solving One-Step Equations
Use inverse operations to solve one-step
equations.
The Properties of Equality
For any numbers a, b and c:
Subtraction Property of Equality
If a = b, then a – c = b – c
Addition Property of Equality
If a = b, then a + c = b + c
Multiplication Property of Equality
If a = b, then ac = bc
Division Property of Equality
a b
If a = b, then 
c c
Explore!
Introduction to Equation Mats
Step 1 If you do not have an equation mat, draw one like the one seen below on a
blank sheet of paper.
Step 2 On your equation mat, place a variable cube on one side with 3 negative
integer chips. On the other side of the mat, place 5 positive integer chips. This
represents the equation x − 3 = 5.
Explore!
Introduction to Equation Mats
Step 3 In order to get the variable by itself, you must cancel out the 3 negative integer
chips with the variable. Use zero pairs to remove the chips by adding three
positive integer chips to the left side of the mat. Whatever you add on one side
of the mat, add on the other side of the mat. This is using the Addition Property
of Equality. How many chips are on the right side of the mat? What does this
represent?
Step 4 Clear your mat and place chips and variable cubes on the mat to represent the
equation 4x = −8. Draw this on your own paper.
Step 5 Divide the integer chips equally among the variable cubes. This is using the
Division Property of Equality. Each variable cube is equal to how many
integer chips? Write your answer in the form x = ___.
Good to Know!

You can solve equations using inverse operations to keep your equation
balanced. Inverse operations are operations that undo each other, such as
addition and subtraction.

Even though you may be able to solve many one-step equations mentally, it
is important that you show your work. The equations you will be solving in
later lessons and in future math classes will become more complex.

Drawing a vertical line through the equals sign can help you stay organized.
Whatever is done on one side of the line to cancel out a value must be done
on the other side.
Example 1
Solve each equation. Show your work and check your solution.
a. x + 13 = 41
The vertical line can help
you stay organized.
The inverse operation of
addition is subtraction.
Subtract 13 from both sides
of the equation to isolate
the variable.
 Check the answer by substituting
the solution into the original equation
for the variable.
x + 13 = 41
–13 –13
x = 28
(28) + 13 = 41
41 = 41
Example 1 Continued…
Solve each equation. Show your work and check your solution.
b. 6m = 27
Divide both sides of the
equation by 6.
 Check the solution.
6m = 27
6
6
1
m = 4.5 or m = 4 2
6(4.5) = 27
27 = 27
Example 1 Continued…
Solve each equation. Show your work and check your solution.
y
c.  4  
3
The variable can be on
either side of the equation.
Multiply both sides of
the equation by 3.
y
3   4    3
3
12  y
 Check the solution.
(12)
 4 
3
4  4
?
Example 2
The meteorologist on Channel 3 announced that a record
high temperature has been set in Kirkland today. The new
record is 2.8º F more than the old record. Today’s high
temperature was 98.3º F. What was the old record?
Let x represent the old record temperature.
The equation witch represents the situation is:
Subtract 2.8 from each side of the equation
to isolate the variable.
 Check
The old record high temperature in Kirkland was 95.5º F.
x + 2.8 = 98.3
x + 2.8 = 98.3
– 2.8 – 2.8
x = 95.5
95.5 + 2.8 98.3
98.3 = 98.3
Communication Prompt
How are inverse operations useful when solving
equations?
Formative Assessment 4.2
Solve each equation. Show your work and check your
solution.
1. x + 39 = 150
x = 111
2. d  3
5
d = –15
3. 12.9 = y – 14.2
y = 27.1
4. –5t = 55
t = –11