1. Solving Multi-Step Equations
Integrated MATHEMATICS

2. Objectives
Students will calculate the value of an unknown term of a multistep equation through the combination of like-terms.

3. Multi-Step Equations 1) Separate the Equation 2) Simplify
A) Distributive Property
B) Combine Like-Terms
3) Should It Stay or Should It Go (Variables on Left/Constants on Right)
4) Solve for Variable

4. Multi-Step Equations
Ex. 1) 7𝑥+3−4𝑥+1=10

5. Multi-Step Equations
Ex. 2) 4𝑛−1+3𝑛=10

6. Multi-Step Equations
Ex. 3) −29=−6𝑛+5−4+𝑛

7. Multi-Step Equations
Ex. 4) 2𝑥+4 x−3 =18

8. Multi-Step Equations
Ex. 5) −135=3 1−5𝑝 −8𝑝

9. Multi-Step Equations
Ex. 6) 9=−7 7𝑛−1 +2(𝑛+1)

10. Multi-Step Equations
Ex. 7) −5 6𝑝−1 −5 1+8𝑝 =−70

11. Try These 4𝑥−10−1−3𝑥=−20 42 = −5(8n − 1)2(n − 2)
−2(3p + 1) − 4(2 − 3p) = 50

12. Multi-Step Equations 1) Separate the Equation 2) Simplify
A) Distributive Property
B) Combine Like-Terms
3) Should It Stay or Should It Go (Variables on Left/Constants on Right)
4) Solve for Variable

13. Multi-Step Equations
Ex. 9) 3+5𝑥=6𝑥−7−2𝑥

14. Multi-Step Equations
Ex. 10) 7𝑥+3=2(5𝑥+3)

15. Multi-Step Equations
Ex. 11) 3(7 + 2x) = (x – 1)

16. Multi-Step Equations
Ex. 12) 4(3 + 5y) – 4 = 3 + 2(y – 2)

17. TRY THESE 1) 8𝑥+6−2𝑥=−12−4𝑥−2 2) 4d – 8 – d = 6 - d 3) 3 𝑓+4 −5=−5+12
4) 4v + 5v – 4 = v
−𝟐 −𝟏−𝟐𝒂 =𝟑(𝒂+𝟔)
6. 𝟒 𝒙−𝟓 +𝟐 𝒙+𝟏 =𝒙−𝒙

18. Objectives
Students will calculate the value of an unknown term of a multistep equation through the combination of like-terms.
Students will differentiate between equations that have no solution and an infinite number of solutions.

19. Solutions to Linear Equations
An equation with one variable may have: 
Exactly One Real Solution
Infinite Real Solutions (Identity)
No Real Solution

20. Multi-Step Equations
Ex. 1) 5x – 2 = 8x + 4 – 3x

21. Multi-Step Equations
Ex. 2) 2(4 + x) = 2x – 6

22. Multi-Step Equations
Ex. 3) 7x – 3 + 5x = 2(6x + 3) – 9

23. Multi-Step Equations
Ex. 4) 3m + 3 = 3(m – 2) + 9

24. TRY THESE 1) 3x – 9 + 5x = 2(6x + 3) – 4x 2) 3d – 8 – 2d = 6 – d
3) 3 𝑓+2 −5=1+3𝑓
4) 4v + 5v – 8 = 3v – v + 2
12t + 2 – 15t = –3t – 2