1. Solving One-Step Equations
Created by Ita Rodríguez

2. Equations An equation is a mathematical sentence with an equal sign.
𝑥+5=3
If it doesn’t have an equal sign, it is not an equation!
𝑦− algebraic expression

3. Equations
Operations are addition, subtraction, multiplication, and division.
Inverse operations are opposites of each other.
addition subtraction multiplication division
Equations are solved using inverse operations.

4. Solving Equations by Adding or Subtracting
Solve 𝑥+5=3.
Step 1: Identify which side of the equation the variable is on.
Left side
Step 2: Identify what is being done to the variable.
Adding 5
Step 3: What is the opposite or inverse operation?
Subtracting 5
Now we are ready to use algebra tiles!

5. Solving Equations by Adding or Subtracting
Solve 𝑥+5=3.
Step 1: Identify which side of the equation the variable is on. =
Left
Step 2: Identify what is being done to the variable.
Adding 5 or Positive 5

6. Solving Equations by Adding or Subtracting
Solve 𝑥+5=3.
Step 3: What is the opposite or inverse operation? =
Subtract 5 or Negative 5
Step 4: Balance the equation by doing the opposite or inverse operation on both sides.
= 𝑥+5=3
−5 −5

7. Solving Equations by Adding or Subtracting
Solve 𝑥+5=3.
Step 5: Solve the equation on both sides.
= 𝑥+5 = 3
−5 −5
0 −2
= 𝑥 = −2

8. Solving Equations by Adding or Subtracting
Solve 12=𝑦−7.
Step 1: Identify which side of the equation the variable is on. =
Right
Step 2: Identify what is being done to the variable.
Subtracting 7 or Negative 7

9. Solving Equations by Adding or Subtracting
Solve 12=𝑦−7.
Step 3: What is the opposite or inverse operation? =
Adding 7 or Positive 7
Step 4: Balance the equation by doing the opposite or inverse operation on both sides.
= =𝑦−7

10. Solving Equations by Adding or Subtracting
Solve 12=𝑦−7.
Step 5: Solve the equation on both sides.
= =𝑦−7
= =𝑦

11. Solving Equations by Multiplying or Dividing
Solve 3𝑚=−6.
Step 1: Identify which side of the equation the variable is on. =
Left
Step 2: Identify what is being done to the variable.
Multiplying (3 groups of tiles)

12. Solving Equations by Multiplying or Dividing
Solve 3𝑚=−6.
Step 3: What is the opposite or inverse operation? =
Divide 3
Step 4: Balance the equation by doing the opposite or inverse operation on both sides.
= 𝑚 3 = −6 3

13. Solving Equations by Multiplying or Dividing
Solve 3𝑚=−6.
Step 5: Solve the equation on both sides.
= 𝑚 3 = −6 3
= 𝑚=−2

14. Solving Equations by Multiplying or Dividing
Solve 𝑘 2 =−4.
(Because 𝑘 2 means half a variable tile, we cannot use algebra tiles to solve. Instead, we will draw a representation.)
A variable k is being divided into 2 parts. k

15. Solving Equations by Multiplying or Dividing
Solve 𝑘 2 =−4.
We are told by the equation that each value of k is −4. k
We can see there are 2 groups − (−4)= −8
So k= −8. −4 −4

16. Solving Equations by Multiplying or Dividing
Solve 𝑘 2 =−4. Now we’ll solve algebraically.
Step 1: Identify which side of the equation the variable is on.
Left
Step 2: Identify what is being done to the variable.
Dividing 2

17. Solving Equations by Multiplying or Dividing
Solve 𝑘 2 =−4.
Step 3: What is the opposite or inverse operation?
Multiply 2
Step 4: Balance the equation by doing the opposite or inverse operation on both sides.
2 1 ∙ 𝑘 2 =−4∙ 2 1

18. Solving Equations by Multiplying or Dividing
Solve 𝑘 2 =−4.
Step 5: Solve the equation on both sides.
2 1 ∙ 𝑘 2 =−4∙ 2 1
𝑘=−8

19. Good luck!
Now you try