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