1. Bell Ringer (NWEA) RIT band 231-240

2. Solving Equations: variables on BOTH sides
The student will be able to:
1. solve equations with variables on both sides.
2. solve equations containing grouping symbols.

3. 1) Solve. 3x + 2 = 4x - 1
You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

4. Rules to remember Simplify the left and the right separately
Use combining like terms and distribution
Solve by using inverse operations.
If you are moving anything over the equal sign, use inverse operations. If you are simplifying the separate sides, DO NOT use inverses

5. 1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x
3 = x
3(3) + 2 = 4(3) - 1
9 + 2 =
Draw “the river”
Subtract 3x from both sides
Simplify
Add 1 to both sides
Check your answer

6. 2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11
11y =
y = 1
8(1) - 9 = -3(1) + 2
Draw “the river”
Add 3y to both sides
Simplify
Add 9 to both sides
Divide both sides by 11
Check your answer

7. What is the value of x if 3 - 4x = 18 + x?-3 3
Answer Now

8. 3) Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1) Draw “the river”
1 = x
4 = 7(1) - 3(1)
Draw “the river”
– Notice the variables are on the same side!
Combine like terms
Divide both sides by 4
Simplify
Check your answer

9. Let’s Throw in some Combining Like Terms!!!

11. That’s All for Today!!!
Please do your DLIQ!!!

12. Bell Ringer

13. Homework Review

14. YOU HAVE A QUIZ ON FRIDAY!!!!!
This quiz will cover the following:
1 step Equations
2 step easy equations
2 step 2 “floor” equations
Multistep equations
Multistep equations with variables on both sides

15. 4) Solve -7(x - 3) = -7 -7x + 21 = -7 - 21 - 21 -7x = -28 -7 -7 x = 4
-7x = -28
x = 4
-7(4 - 3) = -7
-7(1) = -7
Draw “the river”
Distribute
Subtract 21 from both sides
Simplify
Divide both sides by -7
Check your answer

16. What is the value of x if 3(x + 4) = 2(x - 1)?
-14
-13 13 14
Answer Now

17. 5) Solve 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6
Draw “the river”
Clear the fraction – multiply each term by the LCD
Simplify
Add 2x to both sides
Add 6 to both sides
Divide both sides by 6
Check your answer
3 - 2x = 4x – 6
+ 2x +2x
= 6x – 6
= 6x
or 1.5 = x

18. -2x -2x 5 = -3 This is never true! No solutions
Special Case # ) 2x + 5 = 2x - 3
-2x x
5 = -3
This is never true!
No solutions
Draw “the river”
Subtract 2x from both sides
Simplify

19. Infinite solutions or identity
Special Case # ) 3(x + 1) - 5 = 3x - 2
3x + 3 – 5 = 3x - 2
3x - 2 = 3x – 2
-3x x
-2 = -2
This is always true!
Infinite solutions or identity
Draw “the river”
Distribute
Combine like terms
Subtract 3x from both sides
Simplify

20. What is the value of x if -3 + 12x = 12x - 3?4
No solutions
Infinite solutions
Answer Now

21. Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2?-2 2 8
Answer Now