Equivalent Expressions

Equivalent Expressions

How can you identify equivalent algebraic expressions?

Multiple Choice

Use the Distributive Property to write an equivalent expression:

 $2\left(4x+3\right)$  

• 8x + 3

• 6x + 3

• 8x + 6

• 6x + 6

1. Multiply the outside with the 1st number.

2. Multiply the outside with the 2nd number.

3. Put the two together and add the operation from the parenthesis.

 $2\left(4x+3\right)=8x+6$  
These are known as equivalent expressions.

• They have the same value. 

• You can check if they are equal by substituting X with a number.

Multiple Choice

Which expression is equivalent to:

 $2x+6$  

•  $2\left(x+3\right)$ 

•  $x+1+x+2$  

 $2x+6$  
Substitute X in each expression to check the value. (Make x = 2)
 $2x+6=2\cdot2+6=4+6=10$  

•  $2\left(x+3\right)=2\left(2+3\right)=2\left(5\right)=10$  -- YES! This is equivalent!

•  $x+1+x+2=2+1+2+2=7$  -- NO! This is not equivalent.

Multiple Choice

Which expression is equivalent to:

 $2\left(x+2\right)$  

• 2x + 2

• 2x + 4

 $2\left(x+2\right)=2\left(2+2\right)=2\left(4\right)=8$  

Substitute X for 2 and compare values:

•  $2x+2=2\cdot2+2=4+2=6$  -- No! This is not equal to 8. 

•  $2x+4=2\cdot2+4=4+4=8$   -- Yes! This is equal to 8!

Let's Compare Another Way!

• Simplify each expression by combining like terms.

• Compare the simplified expressions.

Multiple Select

Choose all expressions that are equal to:

 $5\left(2x+3\right)$  

•  $10x+15$  

•  $5x+15+5x$  

•  $10x+8$  

Multiple Select

Choose all expressions that are equal to:

 $4x-8$  

•  $2\left(2x-6\right)$  

•  $2\left(2x-4\right)$  

•  $x-8+3x$  

Multiple Select

Choose all expressions that are equal to:

 $12x-16$  

•  $9x-16+3x$  

•  $3\left(3x-5\right)$  

•  $4\left(3x-4\right)$  

Poll

How are you feeling about finding Equivalent Expressions?

• Great!

• So-So

• Confused