Objective - To solve simple equations
involving addition and subtraction.
50 5
8  0  8
0  23  23
Identity Property of Addition
x0 x
additive identity
Equation - A mathematical sentence that shows two
expressions are equal.
8+4
=
12
“fulcrum”
Equations must always stay perfectly balanced.
Determine which value is the correct solution to
the equation.
1) 8  x  13
3) 12  p  5
x  3, 5, 7, or 8
p  3, 4, 7, or 8
x 5
p7
2) m  9  20
4) t  14   11
m   10, 4, 8, or 11
m  11
t   7,  3, 3, or 11
t 3
Addition Property of Equality
If a = b, then a + c = b + c
or
Given a = b
and c = c
then a + c = b + c
Subtraction Property of Equality
If a = b, then a - c = b - c
or
Given a = b
and c = c
then a - c = b - c
x+3
-3
=
7
Heavier
x
=
7
Heavier
x
=
7
Heavier
x
=
7
Heavier
x
=
7
Heavier
x+3
-3
=
7
-3
x
=
4
Algebraically,
x+3=7
-3 -3
x=4
x+3=7
x+3-3=7-3
x=4
1) Goal: Isolate the variable on one side
of the equation.
2) Always perform the same operation to
both sides of an equation.
3) To undo an operation, perform its opposite
operation to both sides of the equation.












Solve the equations below.
1) x + 3 = 10
-3 -3
x=7
4) 13 = x + 5
-5
-5
8=x
2) y - 8 = 11
+8 +8
y = 19
5) 12 = n - 3
+3
+3
15 = n
3) n + 5 = 11
-5 -5
n=6
6) 11 + 3 = k
14 = k
Translate the sentence into an equation and solve.
1) The sum of k and 13 is 28.
k + 13 = 28
- 13 - 13
k = 15
2) Five is the difference of t and 4.
5=t-4
+4
+4
9=t
Five-Step Plan
1) Read the problem.
•Draw a picture.
•Make a chart.
2) Determine the unknowns.
•Define an unknown with a variable.
•Define all other unknowns in terms
of first variable.
3) Write an equation involving the variable.
4) Solve the equation.
5) Check your answer.
1) Matt scored a 85 on his last test. This is 16
points higher than he scored on his first test.
What was his score on the first test?
Let t = first test score
85  16  t
16  16
69  t
first test sco re  6 9
Define a variable, write an algebraic equation,
and solve.
2) A gazelle can run at a speed of 50 mph. This
is 10mph slower than the speed of a cheetah.
What is the speed of a cheetah?
Let x = the speed of a cheetah
50 = x - 10
+10
+10
60 = x
cheetah speed = 60
Define a variable, write an algebraic equation,
and solve.
3) The Sears Tower is 110 stories tall. This is
8 stories taller than the Empire State Building.
How many floors is the Empire State Building?
Let x = the # of stories in Empire State
110 = x + 8
-8
-8
102 = x
# Floors in Empire State = 102
Define a variable, write an algebraic equation,
and solve.
4) A submarine is 50 meters below the surface
of the ocean. A scuba diver is 5 meters below
the surface. Write an equation to find their
difference in elevation and solve.
Let x = difference in elevation
-50 + x = -5
+50
+50
x = 45
Difference in elevation = 45