One-Step Equations Vocabulary
Equation – a mathematical
sentence that contains an
equal sign. The equation acts
like a bal...
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.
We solve one-step
equations by performing
the opposite operation
or “inverse operation.”
Addition
Subtractio
n
Multiplicat...
Inverse operations- two
operations that have the
opposite effect
Addition

Subtraction

Multiplication

Division
Let’s look at it using
algebra

Step 1:
Complete
the inverse
operation to
both sides
of the
equation.

x + 10 = 15
- 10 10...
Step 3:
Check the
solution by
“substituting” or
Solving
One-Step
Addition Equations
What if the
equation were
written this way?

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

x+1=7
Subtraction
To keep the equation
balanced…..
….we must perform the same
operation to both sides.
Since this is addition,
we subtract the same number
from both sides.

X+1=7
-1 -1
X+1=7
-1 -1
X

=6
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 variabl...
Example 1 (bar model)

m + 18 = 34
m

18

Look for variable
Do the inverse
What number does m represent?

34

m = 16

Subs...
Solving One-Step
Subtraction Equations
What if the equation
were written this
way?

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

x–1=8
Addition
To keep the equation
balanced…..
….we must perform the same
operation to both sides.
Since this is subtraction,
we add the same number to both
sides.

x–1= 8
+ 1 +1
x–1= 8
+ 1 +1
=9
X
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
Solving One-Step
Multiplication Equations
What if the equation
were written this
way?

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

2x = 12
Division
To keep the equation
balanced…..
….we must perform the same
operation to both sides.
Since this is multiplication,
we divide both sides by the same
number.

2x = 12
2
2
2x = 12
2
2
X =6
Solving
One-Step
Division Equations
What if the equation
were written this
way?

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

x -2=4
Multiplication
To keep the equation
balanced…..
….we must perform the same
operation to both sides.
Since this is division,
we multiply both sides by
the same number.

x–2=4
2(x – 2) = 2(4)
x– 2=4
2(x – 2) = 2(4)
X

= 8
A check only takes 3 steps:
1. Write the original equation.
2. Substitute the answer
for the variable.
3. Verify that both...
Your Turn: Practice Worksheets 1- 4
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One step equations for 6th grade (positive numbers)

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One step equations for 6th grade (positive numbers)

  1. 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. 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. 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. 4. Inverse operations- two operations that have the opposite effect Addition Subtraction Multiplication Division
  5. 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. 6. Step 3: Check the solution by “substituting” or
  7. 7. Solving One-Step Addition Equations
  8. 8. What if the equation were written this way? x+1=7
  9. 9. Which operation should we choose to solve? x+1=7 Subtraction
  10. 10. To keep the equation balanced….. ….we must perform the same operation to both sides.
  11. 11. Since this is addition, we subtract the same number from both sides. X+1=7 -1 -1
  12. 12. X+1=7 -1 -1 X =6
  13. 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. 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. 15. Solving One-Step Subtraction Equations
  16. 16. What if the equation were written this way? x–1=8
  17. 17. Which operation should we choose to solve? x–1=8 Addition
  18. 18. To keep the equation balanced….. ….we must perform the same operation to both sides.
  19. 19. Since this is subtraction, we add the same number to both sides. x–1= 8 + 1 +1
  20. 20. x–1= 8 + 1 +1 =9 X
  21. 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. 22. Solving One-Step Multiplication Equations
  23. 23. What if the equation were written this way? 2x = 12
  24. 24. Which operation should we choose to solve? 2x = 12 Division
  25. 25. To keep the equation balanced….. ….we must perform the same operation to both sides.
  26. 26. Since this is multiplication, we divide both sides by the same number. 2x = 12 2 2
  27. 27. 2x = 12 2 2 X =6
  28. 28. Solving One-Step Division Equations
  29. 29. What if the equation were written this way? x -2=4
  30. 30. Which operation should we choose to solve? x -2=4 Multiplication
  31. 31. To keep the equation balanced….. ….we must perform the same operation to both sides.
  32. 32. Since this is division, we multiply both sides by the same number. x–2=4 2(x – 2) = 2(4)
  33. 33. x– 2=4 2(x – 2) = 2(4) X = 8
  34. 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. 35. Your Turn: Practice Worksheets 1- 4

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