1. Bell Ringer Solve the following: 1. ) 7(4 – t) = -84 2
Bell Ringer Solve the following: 1.) 7(4 – t) = ) 78 = 3c +12 – c + 4 Go over homework from yesterday
Pg even

2. 6-4 Solving Equations with the Variable on Both Sides
Objectives:
to solve equations with the variable on both sides.
to solve equations containing grouping symbols.

3. To solve for a variable the variable must be positive with no number beside it!! 
x = 10 Solved - x = -5 Not solved 2x = 5 Not solved -3x =6 Not solved Bottom page of notes

4. To solve these equations,
Use the addition or subtraction property to move all terms from one side of the equal sign to another.
6x - 3 = 2x + 13
-2x x
4x - 3 = 13
Use the multiplication or division to bust a term up. (Separate the coefficient (number) from the variable (letter))
4x = 16
x = 4

5. Let’s see a few examples:
Make variable on 1 side of equation (do it so the variable is positive)
1) 6x - 3 = 2x x -2x 4x - 3 = x = x = 4
Be sure to check your answer! 6(4) - 3 = 2(4) = = 21

6. Let’s try another!
Check: 3(1.5) + 1 = 7(1.5) = = 5.5
2) 3n + 1 = 7n n -3n 1 = 4n = 4n 4 4 Reduce! 3 = n 2 Rewrite as n = 3/2

7. Here’s a tricky one! 3) 5 + 2(y + 4) = 5(y - 3) + 10
Distribute first.
5 + 2y + 8 = 5y
Next, combine like terms.
2y + 13 = 5y - 5
Now solve. (Subtract 2y.)
13 = 3y (Add 5.)
18 = 3y (Divide by 3.)
6 = y Rewrite as y = 6
Check: 5 + 2(6 + 4) = 5(6 - 3) (10) = 5(3) = = 25

8. Let’s try one with fractions!
Steps:
Multiply each term
by the least common
denominator (8) to
eliminate fractions.
Solve for x.
Add 2x.
Add 6.
Divide by 6.
3 - 2x = 4x = 6x = 6x so x = 3/2
2 *
1 *
2 *
4 *

9. (Notice there’s no variable at all in both cases.)
Two special cases:
6(4 + y) - 3 = 4(y - 3) + 2y y - 3 = 4y y y = 6y y - 6y 21 = -12 Never true! 21 ≠ -12 Write ………. NO SOLUTION!
3(a + 1) - 5 = 3a - 2 3a = 3a - 2 3a - 2 = 3a a -3a -2 = -2 Always true! We write IDENTITY.
(Notice there’s no variable at all in both cases.)

10. Try a few on your own: 9x + 7 = 3x - 5 8 - 2(y + 1) = -3y + 1
8 - 1 z = 1 z - 7

11. The answers:
x = -2
y = -5
z = 20

12. Page , and 24 even
Show your steps