1. Objective
3.4 solve equations with variables on both sides

2. Equation- mathematical sentence with an equal sign Like a scale,
both sides must be
EQUAL in order
to be balanced.

3. Solving Equations with Variables on Both Sides
How can you get the “unknown” by itself?
7 - 8x = 4x – 17
Solving Equations with Variables on Both Sides
STEP 1- Use distributive property and combine like terms.
STEP 2- Collect variables on one side of the equation.
STEP 3- “Undo” addition and/or subtraction.
STEP 4- “Undo” multiplication and/or division.
STEP 5- Solve for the variable.
STEP 6- Check your work.

4. Solving Equations with Variables on Both Sides…
Isolate the variable! Get ‘x’ by itself.
7 – 8x = 4x – 17.
Write original equation.
7 – 8x + 8x = 4x – x
Add 8x to each side.
7 = 12x – 17
Simplify each side.
24 = 12x
Add 17 to each side.
2 = x
Divide each side by 12.

5. 7 – 8x = 4x – 17 x = 2 7 – 8(2) = 4(2) – 17 Are both sides equal?
Check Your Work!
7 – 8x = 4x – 17
x = 2
7 – 8(2) = 4(2) – 17
Are both sides equal?

6. Solving Equations with Variables on Both Sides…
Isolate the variable! Get ‘x’ by itself.
9x – 5 = 1 4
(16x + 60). 1 4
(16x + 60).
9x – 5 =
Write original equation.
9x – 5 = 4x + 15
Distributive property
5x – 5 = 15
Subtract 4x from each side.
5x = 20
Add 5 to each side.
x = 4
Divide each side by 5.

7. 9x – 5 = ¼ (16x + 60) x = 4 9(4) – 5 = ¼ (16(4) + 60)
Check Your Work!
9x – 5 = ¼ (16x + 60)
x = 4
9(4) – 5 = ¼ (16(4) + 60)
Are both sides equal?

8. Solving Equations with Variables on Both Sides…If Possible
Isolate the variable! Get ‘x’ by itself.
2 – 15n = 5(-3n +2)
3x +10 – x = 2(x +5)
2 – 15n = -15n + 10
2x + 10 = 2(x+5)
2 – 15n +15n = -15n +15n + 10
2x + 10 = 2x + 10
2 = 10
Identity
No Solution

9. Guided Practice 2) -17p – 6 = -38 – p 1) 6x + 11 = 2x – 5

10. Guided Practice 7p + 6 – 3p = -38 + 4p 4 + 2x + 8 = 2(x + 6)
6 ≠ -38
2x + 12 = 2x + 12
No solution
Identity
All numbers

11. Geometry Connection Find the area and perimeter of the square.
4x – 2
4x – 2 = 3x + 7
4x – 3x = 7 + 2
3x + 7
x = 9
The perimeter of the square is 34(4) which is 136 units.
The area of the square is 34 x 34 which is 1156 square units.

12. Homework
Text p. 150& odds
Quiz Friday: Multi-Step Equations