1) Algebraic expressions and equations can be solved through various operations including addition, subtraction, multiplication, division, and combinations of these operations. 2) Negative numbers require inverse operations - for example, to isolate a negative term we must add instead of subtract. 3) Solving multi-step equations may require distributing terms, combining like terms, and isolating the variable using inverse operations on both sides of the equation.

1. Sweet
Algebra!

2. Key
= +x = +1
= -x = -1

3. t 2 4 Addition or Positive

4. t 2 4 Addition or Positive
2 2
t 2
Take away… …from both sides.

5. 2 3 t Subtraction or Negative
There are no
negatives to
take away…

6. 2 3 t Subtraction or Negative
3 3 …so we have to add three positives to both sides...
…making zero pairs on the right
that cancel out each other.

7. 2 3 t Subtraction or Negative
3 3
5 t

8. 2t 6 Negative Multiplication

9. 2t 6 Negative Multiplication
2 2
t 3
Split… …into two groups...

10. 2t 6 Negative Multiplication
2 2
t 3
t 3
…then take the inverse… …of both sides.

11. t Negative Division
3
2
We only have half
a negative bear…

12. t Negative Division
2 3 2
2
…on both sides…
…so we have to
double what we
have…

13. t 6 Negative Division
…to get one whole
negative bear…

14. t 6 Negative Division
t 6
…of both sides.
…then take the inverse…

15. 6 2t 2 Two-Step

16. 6 2t 2 Two-Step
2 2
4 2t
Take away… …from both sides...

17. 6 2t 2 Two-Step
2 2
4 2t
2 2
2 t
…then split… …into two groups

18. 2(t 1) 4 t Multi-Step with Distribution
The two on the outside of the
parenthesis means we need to
have two groups of t + 1.

19. 2(t 1) 4 t Multi-Step with Distribution
2t 2 4 t
We then need the variables
to be moved to one side…

20. 2(t 1) 4 t Multi-Step with Distribution
2t 2 4 t
t t
3t 2 4
…adding a positive bear …making a zero
to both sides… pair on the right.

21. 2(t 1) 4 t Multi-Step with Distribution
2t 2 4 t
t t
There are no positives to
3t 2 4 take away on the right, so we
2 2 add two negatives to both sides…
3t 6
…making zero pairs
on the left that cancel
out each other.

22. 2(t 1) 4 t
Multi-Step with Distribution
2t 2 4 t
t t
3t 2 4
2 2
3t 6
3 3
t 2
Now split… …into three groups.