This document provides an overview of one-step equations and their solutions. It defines key terms like equation, solution, and inverse operations. It then demonstrates how to solve one-step addition, subtraction, multiplication, and division equations by performing the inverse operation to both sides of the equation to isolate the variable. Examples are provided and it emphasizes that the solution is checked by substituting the answer back into the original equation.

1. One-Step Equations Vocabulary
Equation – a mathematical
sentence that contains an
equal sign. The equation acts
like a balance scale.
Solution – a number that can
replace a variable in an
equation and make a true
statement.
Algebra- A branch of

2. Since an equation is like a balance scale, if you do
something to one side, then you have to
do it to the other side.

3. We solve one-step
equations by performing
the opposite operation
or “inverse operation.”
Addition
Subtractio
n
Multiplicatio
n
Division
Subtractio
n
Addition
Division
Multiplication

4. Inverse operations- two
operations that have the
opposite effect
Addition
Subtraction
Multiplication
Division

5. Let’s look at it using
algebra
Step 1:
Complete
the inverse
operation to
both sides
of the
equation.
x + 10 = 15
- 10 10 = 5
x
Step 2:
Write or
“bring down”
the result.

6. Step 3:
Check the
solution by
“substituting” or

7. Solving
One-Step
Addition Equations

8. What if the
equation were
written this way?
x+1=7

9. Which operation
should we choose
to solve?
x+1=7
Subtraction

10. To keep the equation
balanced…..
….we must perform the same
operation to both sides.

11. Since this is addition,
we subtract the same number
from both sides.
X+1=7
-1 -1

12. X+1=7
-1 -1
X
=6

13. Example 1
m + 18 = 34
-18 -18
m = 16
Do the inverse
m + 18 = 34
16 + 18 = 34
34 = 34
substitute in m
Look for variable
Write what m is
Solution is correct!

14. Example 1 (bar model)
m + 18 = 34
m
18
Look for variable
Do the inverse
What number does m represent?
34
m = 16
Substitute in m
16
18
34
16 + 18 = 34
34 = 34
Solution is correct!

15. Solving One-Step
Subtraction Equations

16. What if the equation
were written this
way?
x–1=8

17. Which operation
should we choose
to solve?
x–1=8
Addition

18. To keep the equation
balanced…..
….we must perform the same
operation to both sides.

19. Since this is subtraction,
we add the same number to both
sides.
x–1= 8
+ 1 +1

20. x–1= 8
+ 1 +1
=9
X

21. Try These...
1.
2.
3.
4.
r + 5 = 18
m - 26 = 59
102 = x - 15
a + 39 = 56
r = 13
m = 85
117 = x
a = 17

22. Solving One-Step
Multiplication Equations

23. What if the equation
were written this
way?
2x = 12

24. Which operation
should we choose
to solve?
2x = 12
Division

25. To keep the equation
balanced…..
….we must perform the same
operation to both sides.

26. Since this is multiplication,
we divide both sides by the same
number.
2x = 12
2
2

27. 2x = 12
2
2
X =6

28. Solving
One-Step
Division Equations

29. What if the equation
were written this
way?
x -2=4

30. Which operation
should we choose to
solve?
x -2=4
Multiplication

31. To keep the equation
balanced…..
….we must perform the same
operation to both sides.

32. Since this is division,
we multiply both sides by
the same number.
x–2=4
2(x – 2) = 2(4)

33. x– 2=4
2(x – 2) = 2(4)
X
= 8

34. A check only takes 3 steps:
1. Write the original equation.
2. Substitute the answer
for the variable.
3. Verify that both sides
are equal.
2x = 12
2(6) = 12
12 = 12

35. Your Turn: Practice Worksheets 1- 4