1. Warm-Up
2x + 3 = x + 4

2. Solving Equations with variables on both sides:
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. 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

5. 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

6. 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

7. 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

8. 5) Solve -2(4x – 7) = 3(-2x + 8) -8x + 14 = -6x + 24 + 6x + 6x
-2x = 10
x = -5
-2(4*-5 – 7) = 3(-2*-5 + 8)
-2(-27) = 3(18) or 54 = 54
Draw “the river”
Distribute
Add 6x to both sides
Simplify
Subtract 14 from both sides
Divide both sides by -2
Check your answer

9. 6) 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

10. -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

11. 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

12. What are you struggling with still when solving equations?
Exit Slip
What are you struggling with still when solving equations?