Solve Equations with Variables on Both Sides of Equation

Drag and Drop

List the steps you would take to solve the equation: 4n - 2n = 4​ ​

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Combine Like Terms

Division Property of Equality

Distributive Property

Multiplication Property of Equality

Simplify

Inverse Operations

Transitive Property

Additive Inverse

Solve Equations with Variables on Both Sides of the Equation

​I can justify the steps taken to solve algebraic equations.

5x + 2 = 2x + 14

There are variable terms on both sides of the equation.

To solve, you must decide which variable term to add or subtract to get the variable term on one side only.

Drag and Drop

What is a variable term in the equation 5x + 2 = 2x + 14?​

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5x

2x

2

14

There are two variable terms.

Also positive.
On the right of the equation.

2x

Positive.
On the left of the equation.

5x

Drag and Drop

What are possible first steps would you take to solve the equation: 5x + 2 = 2x + 14.​

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Subtract 5x from both sides.

Subtract 2x from both sides.

Add 5x to both sides.

Add 2x to both sides.

Subtract 2 from both sides. 

Subtract 14 from sides.

Multiple Choice

What equation results from subtracting 5x from both sides of the equation?

5x + 2 = 2x + 14

• 2 = 7x + 14

• 2 = - 3x + 14

• 2 = -7x + 14

• 2 = 2x + 9x

​5x + 2 = 2x + 14

-5x = -5x

2 = -3x + 14

​Subtract 5x from both sides.

Fill in the Blanks

Finish solving the equation.

2 = -3x + 14

Multiple Choice

What if you chose to subtract 2x on both sides instead?

What would be the resulting equation?

5x + 2 = 2x + 14

• -3x + 2 = 14

• 5x + 1x = 14

• 7x + 2 = 14

• 3x + 2 = 14

Multiple Choice

Finish solving the equation: 3x + 2 = 14

• x = 4

• x = 16/3

• x = 14/5

• x = 36

Open Ended

5x + 2 = 2x + 14

If you subtract 5x on both sides first, the resulting equation is 2 = -3x + 14

If you subtract 2x on both sides first, the resulting equation is 3x + 2 = 14

Which first step do you prefer and why?

Multiple Choice

What is the solution of 9 + 2k = -3 - 4k?

• k = 5

• k = 2

• k = -2

• k = -1

Open Ended

In words, explain what steps you would take to solve: 2a + 3 = (1/2)(6 + 4a).

Reorder

To solve: 3a + 1 = -3.6(a - 1)

Reorder the following

• Distribute -3.6 inside the quantity.

• Add 3.6a to both sides.

• Subtract 1 from both sides.

• Divide by 6.6 on both sides.

• a = ?

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Math Response

Solve: 3a + 1 = -3.6(a - 1)

Type answer here

Correct Answer: \frac{13}{33}

Deg^°

Rad

Math Response

Solve: 8a - 4 = -8a + 5a - 15

Type answer here

Correct Answer: -1

Deg^°

Rad