Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Vocabulary

Identity- An equation that is true for every possible value of the variable.

-You can replace the variable with any value and the expressions on each side are equivalent.

Example: x+1=x+1

No Solution-

An equation has no solution if there is no value of the variable that makes the equation true.

Example- x+1=x+2

Learning Objective-

I can solve equations with variables on both sides to identify equations that are identities or have no solution.

Focus Question

How can you solve equations with variables on both sides?

Answer

You can use the properties of equality and inverse operations to write a series of simpler equivalent equations.

 $5x+2=2x+14$  

Steps:
-Write the original equation.
-Subtract 2x from each side. The coefficient 2 is less than the coefficient 5, so it is easier to subtract.
-Simplify. Now there is only one variable term. 
-Subtract 2 from each side.
-Simplify

GOAL!!!

Get the variable on one side of the equation and the numeric terms on the other side!

What is the solution of the equation? Is the equation an identity, or does it not have a solution?

How do you know?

 $3\left(4b-2\right)=-6+12b$  

 $2x+7=-1\left(3-2x\right)$  

Fill in the Blank

 $3a+1=-3.6\left(a-1\right)$ Does the equation have an identity or no solution? 

Multiple Choice

28 + 3r = 10r

• 4

• 7

• 20

• 28

Multiple Choice

30 + 6t = 11t

• 3
• 5
• 6
• 30

Multiple Choice

7x = 3x + 24

• 6
• 10
• 14
• 4

Multiple Choice

What is the first step to solve this equation:
11 - 3x = 44

• Add 3 to both sides
• Subtract 11 from both sides
• Add 11 to both sides
• Divide 3 on both sides.

Multiple Choice

Solve:
3c + 5 = 23

• c = 3
• c = 6
• c = 7
• c = 18

Multiple Choice

Solve the equation:
7x - 4 = 3 + 8x

• x = 7
• x = -7
• x = 2/7
• x = 11

Multiple Choice

Solve for x:
5x - 14 = 8x + 4

• x = 6
• x = -6
• x = -18/13
• x = 10/3