1. Solving Equations with Variables on both sides
Objectives:
To solve equations with variables on both sides of the equal sign.

2. STEPS TO SOLVING LINEAR EQUATIONS
DON’T CALL ME AFTER MIDNIGHT
Distribute
Combine like terms
Move the variables to one side
Add/subtract
Multiply/divide
DCMAM IS A ROAD MAP BUT NOT THE ONLY WAY TO SOLVE AN EQUAITON

3. Which of the following could be the first step?
4x + 27 = 3x
A) Subtract 4x from both sides
B) Subtract 3x from both sides
C) Subtract 27 from both sides
D) Combine like terms (4x and 3x) to get 7x

4. Example 1 Solve. 4x + 27 = 3x -4x -4x 27 = -1x -1 -1 -27 = x
Move variable to one side
-4x x
27 = -1x
Divide on both sides -1 -1
-27 = x

5. How else can we solve example 1?
4x + 27 = 3x
Move variable to one side
-3x x
x + 27 = 0
Subtract on both sides
-27
-27
x = - 27

6. How else can we solve example 1?
4x + 27 = 3x
-27
-27
Subtract on both sides
4x = 3x - 27
Move variable to one side
-3x x
x = - 27

7. Which of the following could be the first step?
3(4 + 4x) = 12x + 12
A) Subtract 12x from both sides
B) Divide each term by 3
C) Distribute
D) Combine (4 and 4x) and (12x and 12)

8. Example 2 Solve. 3(4 + 4x) = 12x + 12 12 + 12x = 12x +12 -12x -12x
distribute
x = 12x +12
notice anything?
-12x -12x
Move variable to one side
12 = 12
ALL REAL NUMBERS
Variables cancel out
End with same number on both sides of =
Means that if you plug in any number into the equation it will work.
What does this answer mean?
NO SOLUTION
Variables cancel out
End with different number on both sides of =
Means that there is no number that will work in the equation.

9. How else can we solve example 2?
Divide each term by 3
Move variable to one side
What does this answer mean?
ALL REAL NUMBERS

10. Which of the following could be the first step?
A) Multiply each term by 4/3
B) Multiply each term by 4
C) Distribute
D) Combine (4 and 3x) and (12 and 8x)

11. Example 3 distribute Move variable to the one side
Subtract to both sides
Divide to both sides

12. How else can we solve Example 3? (Watch)
Multiply all terms by 4
Divide 3 to both sides
Distribute
Move variable to one side
Subtract on both sides
Divide both sides by 4

13. Summary How would you clear the fractions in the following problem?
How do you know whether to move the variables to the left side of the equal sign or the right side?