2. 1-step Equations: + and – 2/27/13
In elementary school, you solved
equations that looked like this:
In Algebra, we just use a variable
instead of the box!
We could rewrite the same equation
like this: x + 3 = 5

3. To solve:
Need to get x by itself.
We must “undo” whatever has been done
to the variable.
Do the same to BOTH SIDES of the = sign!
Answer should be: x = some number.

4. Equations Have to Balance!
Both sides of the = sign must “weigh” the
same!
When you change one side, do the same
to the other side, so it stays balanced!
x + 3 = 7

5. Examples:
Solve each equation. Check your answers!
x + 3 = -7 m – 6 = 8

6. 4 + a = -3
-8 + y = 7

7. 24 = 12 + t
-17 = x – 2

8. You Try!
Solve each equation. Check your answers!
x – 9 = -6 16 + n = 10

9. 1-step Equations: × and ÷ 3/11/13
Just like with adding and subtracting,
we need to “undo” what is done to x.
Use division to “undo” multiplication.
Use multiplication to “undo” division.
Remember: A fraction bar means
divide!
Example: says x divided by 3!

10. Examples:
Solve each equation:
2x = 8
12 = -3b

12. You Try!
Solve each 1-step equation.
-4a = 16

13. Basic 2-Step Equations 3/13/13
A lot like 1-step equations!
Goal: Get x by itself!
Need to “undo” what is done to x.
Always do the same thing to BOTH SIDES!
Use Order of Operations backwards:
Add/Subtract first
Multiply/Divide last

14. Examples:
4x + 7 = 27 – 6 – 2y = 10

15. 5 = 7r - 2 -4 = 2 - m

16. You Try!
Solve each equation. Check your answers!
-3x + 7 = 16 -8 = 2a + 2

17. Multi-Step Equations 3/18/13
Multi-step equations have ( ).
To solve:
Distribute first!!
Then, solve like a 2-step equation!
Example: 4(-x + 4) = 12

18. Examples:
3(– 6 + 3x) = 18
30 = -5(6n + 6)

19. 10 (1 + 3b) = -20
-2 = -(n – 8)

20. Your Try!
-6(1 – 5v) = 54

21. 2 Variables- Same Side 3/21/13
Some equations have variables in more
than one place.
When variables are on the same side of
the = sign:
First, Combine Like Terms
 Like terms may NOT cross the = sign!
Then, solve like a 2-step

22. Examples:
2x + 3x + 1 = 36

23. 3 + 6x – 2x = -5

24. -26 = -7x + 6 + 3x

25. You Try!
Solve for x.
8x – 3x + 7 = 17

26. Variables on Both Sides 3/22/13
To solve equations like this:
2x – 4 = 2 + 5x
1. Get variables together on the left.
 Add or subtract right side x term from
both sides.
2. Solve like a 2-step equation.

27. Examples
9 – 7x = -5x – 7

28. -3x – 7 = 2x – 13

29. You Try!
-3x + 9 = 44 + 4x