The document provides step-by-step instructions for solving basic addition and subtraction equations. It begins by explaining how to isolate the variable by performing the inverse operation to both sides of the equation. Several examples are worked through, showing how to draw a line to separate the equation, perform the operation to both sides, then check the solution. It emphasizes the importance of checking work and provides additional tips for eliminating double signs when variables are combined with addition or subtraction.

1. Objective
The student will be able to:
solve equations using addition and
subtraction.
Designed by Skip Tyler, Varina High School

2. 1) Solve r + 16 = -7
Think of this equation as a balance scale.
Whatever you do to one side has to be done to the
other to keep it balanced!

3. 1) 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 r by itself, we must undo the
“add 16”. What is the opposite of
addition?
Subtract 16

4. 1) Solve r + 16 = -7
- 16 -16
r = -23
-23 + 16 = -7
1. Draw “the river” to
separate the equation
into 2 sides
2. Subtract 16 from both
sides
3. Simplify vertically
4. Check your answer
by substituting your
answer back into the
problem

5. 2) Solve x + 2 = -3
Get the variable by itself. What is your
first step?
1. Add 2 to both sides
2. Subtract 2 from both sides
3. Add 3 to both sides
4. Subtract 3 from both sides
Answer Now

6. 2) Solve x + 2 = -3
- 2 - 2
x = -5
-5 + 2 = -3
1. Draw “the river” to
separate the equation
into 2 sides
2. Subtract 2 from both
sides
3. Simplify vertically
4. Check your answer
by substituting your
answer back into the
problem
On homework and tests, be sure to check your work!!
There is no reason why you should miss a problem!

7. 3) Solve 8 = m - 3
1. m = 5
2. m = 11
3. m = 24
4. m = 8/3
Answer Now

8. 3) Solve 8 = m - 3
+ 3 + 3
11= m
8 = 11 - 3
1. Draw “the river” to
separate the equation
into 2 sides
2. Add 3 to both sides
3. Simplify vertically
4. Check your answer
by substituting your
answer back into the
problem

9. When solving equations, we want to
eliminate double signs.
y + (-3) = 8
is rewritten as
y – 3 = 8
p – (-5) = 6
is rewritten as
p + 5 = 6
As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”.
This will make things less confusing in the future!

10. 4) Solve y + (-3) = 7
y – 3 = 7
+ 3 +3
y = 10
10 + (-3) = 7
1. Draw “the river” to
separate the equation
into 2 sides
2. Eliminate the double
sign
3. Add 3 to both sides
4. Simplify vertically
5. Check your answer
by substituting your
answer back into the
problem

11. 5) Solve. -x - (-2) = 1
-x + 2 = 1
- 2 - 2
-x = -1
x = 1
-(1) + 2 = 1
1. Draw “the river” to
separate the equation into
2 sides
2. Eliminate the double sign
3. Subtract 2 from both sides
4. Simplify vertically
5. We haven’t gotten x by
itself. If we read this
aloud, it is “the opposite
of x equals -1”. What
would x be equal?
6. Check your answer

12. Solve -y – (-3) = 7
1. y = 10
2. y = 4
3. y = -10
4. y = -4
Answer Now