Solving Equations With Variables on Both Sides

1
Solving Equations With Variables on Both Sides

• Lesson Objective
• To use what we already know to solve equations
  with variables on both sides.

2
WARM UP ADVANCED MATH 7

1. Come into the room quietly.
2. Take a Problem Solving w/ Integers worksheet from
   the front of your row.
3. Begin working on the assignment with one partner.
4. You have until 1245 pm

3

• Tools for the Tool Box!!

Distributive Property
Combining like terms
Addition Subtraction Properties of Equality
Multiplication Division Properties of
Equality
4
Steps to Solve Equations with Variables on Both
Sides

• Eliminate ( ) on both sides of equation
• using the distributive property.
• Combine any like terms on both sides.
• Collect variable on one side of the equation
• Collect constants on the other side of the
• equation
• Solve

5
Use Steps to Solve Equation2(x 7) 3 4x - 1

• 2x 14 3 4x 1

2x 17 4x - 1
-2x -2x
17 2x - 1
1 1
4) Collect constants on same side use inverse
operations
18 2x
2 2
9 x
6
Check - replace x with solution2(x 7) 3
4x - 1
2(9 7) 3 4(9) - 1
2(16) 3 4(9) - 1
2) Follow order of operations on both sides of
equation
32 3 36 - 1
35 35
X 9 is the solution to the
equation
7
Use Steps to Solve Equation

• 3x 14 5x 8

-3x -3x
14 2x 8
- 8 - 8
6 2x
4) Collect constants on same side use inverse
operations
2 2
x 3
8
Use Steps to Solve Equation4(1 2x) 4 6x

• 4 8x 4 - 6x

6x 6x
Get variables on same side use inverse
operation (add 6x)
4 - 2x 4
- 4 - 4
-2x 0
-2 -2
x 0
9
Review Steps to Solve Equations with Variables on
Both Sides

• Eliminate ( ) on both sides of equation
• using the distributive property.
• Combine any like terms on both sides.
• Collect variable on one side of the equation
• Collect constants on the other side of the
• equation
• Solve

10

• Tools for the Tool Box!!

Distributive Property
Combining like terms
Addition Subtraction Properties of Equality
Integer Rules
Multiplication Division Properties of
Equality
11
Solve the Equation 6x 2 x 13
12
Solve the Equation 4k 3 3k 4
13
Solve the Equation 3 4x 3x 6
14
Solve the Equation 2(y 3) - 4y - 6
15
Solve the Equation - 2y 5 5(y 2)