1. One & Two Step Equations
Integrated Mathematics

2. Vocabulary
Equation: A statement that the values of two mathematical expressions are equal
Inverse Operations: Operations that undo one another

3. Solving a One-Step Equation
1) Separate the Equation
2) ISOLATE THE VARIABLE:
Should It Stay or Should It Go (Variables on Left/Constants on Right)
Examples:
𝒙=𝟕
𝒚=𝟕𝟐

4. Property of Equality
You can add or subtract any number to BOTH sides of an equation and the equation will still hold true.

5. One-Step Equations with Addition/Subtraction
Ex.1) x + 2 = 6
Ex.2) a – 4 = 2

6. One-Step Equations with Addition/Subtraction
Ex.3) 19 = y + 7
Ex.4) z – 7 = 4

7. One-Step Equations with Addition/Subtraction
Try These:
2) y - 2 = 12
1) x + 4 = 10
3) 15 = 23 + r
4) z = 2

8. Property of Equality
You can multiply or divide BOTH sides of an equation by any number and the equation will still hold true.

9. An Easy Example: (don’t copy)
We all know that 3 = 3.
Does 3(4) = 3? NO!
But 3(4) = 3(4).
The equation is still true if we multiply both sides by 4.
Would you ever put deodorant under just one arm?
Would you ever put nail polish on just one hand?
Would you ever wear just one sock?

10. One-Step Equations with Multiplication/Division
Ex.5) -2x = 8
Ex.6) 3y = 15

11. One-Step Equations with Multiplication/Division
Ex.7) 𝑧 3 = 5
Ex.8) 𝑦 4 = 4

12. What Do We Do with Negative Fractions?
Recall that
The two negatives will cancel each other out.
The two fives will cancel each other out.
− 𝑥 5 = −𝑥 5 = 𝑥 −5
−𝑥 5 =3
Solve
Multiply both sides by -5.

13. One-Step Equations with Multiplication/Division
Try These:
3) 𝑥 5 = 4
1) 25 = 5x
4) - 𝑧 2 = 24
2) -4x = -12

14. Two-Step Equations 1) Separate the Equation
2) Should It Stay or Should It Go
Addition/Subtraction
Multiplication/Division
3) Solve for Variable

15. Two-Step Equations
Ex.9) Solve 5x + 7 = 3

16. Two-Step Equations
Ex.10) Solve 𝑡 = 45

17. Two-Step Equations
Ex.11) Solve 4 = -6y - 20

18. Two-Step Equations
Ex.12) Solve 11z + 8 = 30

19. Two-Step Equations
Ex.13) Solve 4 = 𝑝 −5

20. Two-Step Equations
Ex.14) Solve 20 – c = -9

21. Two-Step Equations
Ex.15) Solve 2𝑥−3 3 =5

22. Two-Step Equations 1) 11x + 2 = 35 4) -32 = 4t - 16 2) 8 = -22 + 2b
Try These:
1) 11x + 2 = 35
4) -32 = 4t - 16
2) 8 = b
5) 𝟒𝒏 𝟓 – 7 = –4
6) 3𝑥+4 2 =5
3) 2 = 5x – 8

23. Write Linear Equations - ADDITION
The SUM of a number and 4
5 MORE than a number
2 PLUS 7
13 ADDED TO a number
A number INCREASED by 9
The SUM of two numbers

24. Write Linear Equations - Subtraction
3 LESS THAN a number
A number DECREASED BY 15
7 MINUS a number
A number Subtracted from 6
The DIFFERENCE BETWEEN two numbers

25. Write Linear Equations - Multiplication The PRODUCT of two numbers
8 TIMES a number
A number MULTIPLIED BY 9
TWICE a number
𝟑 𝟒 𝑶𝑭 a number
The PRODUCT of two numbers

26. Write Linear Equations - Division
The QUOTIENT of 6 and a number
A number DIVIDED by 4
The RATIO of 7 and a number