Solving Linear Equations with Variables on Both Sides: Simplest

Solving Linear ​Equations with Variables on Both Sides: Simplest Case Scenario

By Naomi Anderegg

Our Strategy

(0) Simplify both sides of the equation via distributive property and combining like terms.
(1) Get variables to one side of the equals sign and constants to the other via addition and subtraction to both sides of the equation.
(2) Multiply or divide to finish solving the equation.

Reorder

In what order do we complete these steps?

• Simplify both sides of the equation.

• Get variables & constants to opposite sides of the equals sign via ADDITION & SUBTRACTION.

• Isolate the variable by MULTIPLYING or DIVIDING.

1

2

3

• 1
• 2
• 3

Ex 1: Solve 2x + 28 = 9x -7

Multiple Select

When solving the equation 4x + 8 = 2x - 4, which two of the following would we do in order to get the variables to one side of the equals sign and the constants to the other side?

• subtract 2x from both sides

• add 2x to both sides

• subtract 8 from both sides

• add 8 to both sides

Math Response

Solve 4x + 7 = 2x +21.

Type x = number as your solution.

Type answer here

Correct Answer: x=7

Deg^°

Rad

Ex 2: Solve 2x + 24= 8x -12

Categorize

Options (4)

9

-2

3x

10x

Consider the equation 3x + 9 = 10x -2. Which terms are constant terms? Which terms are variable terms?

Constant terms

Variable terms

Math Response

Solve 3x + 9 = 10x -19

Type answer here

Correct Answer: x=4

Deg^°

Rad

Ex 3: Solve 5x + 36= -x - 6

Multiple Choice

When solving 4x + 9 = -3x -26, which approach would get the variables to the left side of equation?

• adding 3x to both sides

• subtracting 4x from both sides

• subtracting 9 from both sides

• x = -5

Ex 4: Solve 5x + 36= x - 6

Multiple Choice

Solve 7x + 8 = x + 56

• x = 8

• x = 6

• x = -8

• x = -6

Multiple Choice

Find 1/3 + 1/6

• 2/9

• 1/2

• 1/9

Math Response

Solve 2x/3 - 7 = x/3 + 7

Type answer here

Correct Answer: x=42

Deg^°

Rad