2. Solving Equations with Variables on Both Sides 4:3
Write this in your Toolkit.
variables and their coefficients
Goal: Get all on one side of the equal sign.
2x+6 = 3x+2
-2x
AND
Move all of the to the opposite side of the equal sign.
constants
!!!! Important !!!
Use addition or subtraction for these steps!
+6 = x+2 -2
4 = x

3. Remember, you move a positive with a negative.
You move a negative with a positive.

4. Put problem in Toolkit: pg. 237
Question: What should you move? x √
5x = +16
variables and coefficients
-1x
equivalent equation
4  4 = 16
4x = 16
Divide both sides by 4 to remove the multiplying 4.
New, equivalent equation
Question: Now, what?
Does the answer check?
4x = 16
5x = x +16 4 4
5 4 =
x = 4
20 = 20 √

5. 10 = x 20 + 4x = 6x -4x -4x 20 = 2x New, equivalent equation!
𝟐𝟎 𝟐 = 𝟐𝒙 𝟐
10 = x
Check:  10 = 6  10
60 = 60

6. x = 16 -8 - 8 2x = 32 equivalent equation
Pg. 238: Put problems in Toolkit
4x + 8 = 2x + 40
-2x x
2x + 8 = equivalent equation
2x = equivalent equation
𝟐𝒙 𝟐 = 𝟑𝟐 𝟐 Divide by coefficient.
x = 16
Check: 4 = 2  =
72=72 √

7. x = 6 -3x - 3x 6x = 36 equivalent equation
Pg. 238: Also, constants can be moved first.
2. 9x - 2 = x
9x = x equivalent equation
-3x x
6x = equivalent equation
𝟔𝒙 𝟔 = 𝟑𝟔 𝟔 Divide by coefficient.
x = 6
Check: 9 =  6 =
52=52 √ Does 6 work in the equivalent equations?

8. Pg. 238:
x = 7 + 5x
4 + 4x = 5x equivalent equation
-4x - 4x
4 = 1x
4 = x
Check:  4 =  4 =
27=27 √ Does 6 work in the equivalent equations?
4 + 4(4) = 5(4)
= =20 √

9. Pg. 238: Choose your method.
constant or variable/coefficient
x = 4 - 3x x = 4 - 3x
(Remember, 3 is positive!) +x x
-x = 1 - 3x Both are equivalent equations = 4 - 2x
+3x x
2x = Both are equivalent equations = -2x
𝟐𝒙 𝟐 = 𝟏 𝟐 ………Divide by coefficient……… −𝟏 −𝟐 = −𝟐𝒙 −𝟐
x = 𝟏 𝟐 𝟏 𝟐 = x
Check: 3 - 𝟏 𝟐 =  𝟏 𝟐
2 𝟏 𝟐 = 4 - 𝟑 𝟐 … 𝟖 𝟐 - 𝟑 𝟐 = 𝟓 𝟐 = 2 𝟏 𝟐
2 𝟏 𝟐 = 2 𝟏 𝟐 √

10. Pg. 238: Choose your method.
constant or variable/coefficient
9. −x + 4 = −9.8 + x −x + 4 = −9.8 + x
Line up decimals x x
-x = x Both are equivalent equations = −9.8 +2x
-x x Line up decimals = +9.8
−2x = Both are equivalent equations = 2x
−𝟐𝒙 −𝟐 = −𝟏𝟑.𝟖 −𝟐 …Divide by coefficient…… −𝟏𝟑.𝟖 −𝟐 = −𝟐𝒙 −𝟐
x = 𝟔.𝟗 𝟔.𝟗 = x
𝟔.𝟗 𝟐 𝟏𝟑.𝟖
Check: =
= √