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2-5 Solving Equations Containing Integers
Simplify.
1) -23 + (-31)
3)
5–7
5) -7 ● 3
Do Now
2) -19 - (-12)
4) -8 ● -9
6) 54 ÷ (-9)
2-5 Solving Equations Containing Integers
Learn to solve one-step addition and
subtraction equations with integers.
2-5 Solving Equations Containing Integers
Equations are just like a carefully balanced
scale. If both expressions on each side of the
equal sign match, then they are balanced.
2-5 Solving Equations Containing Integers
If one side is heavier than the other,
the scales are tipped.
2-5 Solving Equations Containing Integers
In algebra, we solve equations for the
missing variable. The trick is to keep
the scales balanced during all steps.
Meaning we want both sides to be
EQUAL. In order to do this,
whatever you do to one side of the
equation must be done to the
other.
2-5 Solving Equations Containing Integers
In order to solve for x, we must
isolate (get all by its lonesome self)
the variable.
2-5 Solving Equations Containing Integers
2-5 Solving Equations Containing Integers
2-5 Solving Equations Containing Integers
2-5 Solving Equations Containing Integers
Solving an equation
• What does it mean?
Trying to find the value of the
variable that makes the equation
true
• How?
You want to isolate the variable by
getting the variable alone on one side
of the equal sign
*remember our inverse operations
2-5 Solving Equations Containing Integers
Think of this equation as a balance scale. r + 16 = -7
Whatever you do to one side has to be done to the other
to keep it balanced!
2-5 Solving Equations Containing Integers
Solve.
r + 16 = -7
To solve, you must get the variable by
itself.
What number is on the same side as r?
16
To get rid of 16 we have to use the
inverse operation. What is the opposite
of adding 16?
Subtracting 16
2-5 Solving Equations Containing Integers
1.
2.
3.
4.
Draw “the river” to
separate the
equation into 2
sides
Subtract 16 from
both sides
Simplify
Check your answer
by substituting your
answer back into
the problem
r + 16 = -7
- 16 -16
r
= -23
-23 + 16 = -7
-7 = -7
2-5 Solving Equations Containing Integers
Solving One Step Equations
1. Draw “the river” a line through the equal sign
to separate the two sides of the equation
2. Get rid of anything being added or subtracted
to the variable by doing the inverse operation
(Goal is to have x = ______ in the end)
3. What you do to one side of the equal sign you
must do to the other side to keep it balanced
4. Always check your answers by substituting
into the original equation!!
2-5 Solving Equations Containing Integers
Example B
Solve each equation. Check each answer.
p + 5 = –3
–5
–5
p = –8
Subtract 5 from both sides.
Check
p + 5 = –3
?
–8 + 5 = –3
?
– 3 = –3 
Substitute –8 for p.
True.
2-5 Solving Equations Containing Integers
Example B
Solve each question. Check each answer.
–6 + x = –7
+6
+6
x = –1
Add 6 to both sides to
isolate the variable.
Check
–6 + x = –7
?
–6 + (–1) = –7
?
–7 = –7 
Substitute –1 for x.
True.
2-5 Solving Equations Containing Integers
Example B
Solve each equation. Check each answer.
-40 = y – 9
+9
+9
-31 = y
Add 9 to both sides.
Check
-40 = y - 9
?
–40 = -31 - 9
?
–40 = –40 
Substitute –31 for y.
True.
2-5 Solving Equations Containing Integers
You Try:
Solve each equation. Check each answer.
f -5 = 22
q + 2 = –6
y – 7 = –34
20 = x - 18
m - 16 = –9
–3 + x = –9