Equivalent Equations

Equivalent Equations

Objective: create and identify equivalent equations.

​Vocabulary

Equivalent: to two meanings, numbers, or quantities that are the same.

​

​Examples:

​NOTE: look at each side of the equal sign like it's own seperate entity. NOT like a sentence

​Example 1: Are the following expressions equivalent?

​4 + 2 x 3 - 2 = 44 ÷ 2

​

​

​

​2(x + 9) = 24 + 2x - 15

​?

​?

Multiple Select

Choose all the equivalent expressions.

• $$12+12-3x=3(x+8)$$  

• $$8-3\times3+5=10-12\div2$$  

• $$4x+12=4x+6+6$$  

• $$56\div7=4+3$$  

Open Ended

Are these equivalent?  $$4x+12=4x+6+6$$  ...YES

Are they still equaivalent?  $$4x+12+3=4x+6+6+3$$  ...YES

Why?

​ADDITION PROPERTY OF EQUALITY

​Adding the same number to both sides of an equal sign makes an equivalent equation.

​8 + 5 = 13

is equivalent to

8 + 5 + 4 = 13 + 4

SUBTRACTION PROPERTY OF EQUALITY

​Subtracting the same number from both sides of an equal sign makes an equivalent equation.

​8 + 5 = 13

is equivalent to

8 + 5 - 4 = 13 - 4

​EXAMPLE

​If 5 is added to both sides what is the result?

​

​3x - 15 = 32

Fill in the Blanks

If 7 is subtracted from both sides, what is the result?

$4x+12=24$  

Fill in the Blanks

If 7 is subtracted from both sides, what is the result?

$4x-12=-24$  

​DIVISION PROPERTY OF EQUALITY

Dividing both sides of an equal sign by the same number makes an equivalent equation.

is equivalent to

​10 + 6 = 16

and equivalent to

​EXAMPLE

​If you divide both sides by 3 what is the result?

​

​3x - 15 = 30

Fill in the Blanks

If both sides are divided by 2, what is the result?

$-80=4-18x$  

​EXAMPLE

​Which equations are equivalent to: 16 - 4x = 36

​8 - 2x = 18

​12 - x = 32

​4 - x = 9

Multiple Select

Which equation(s) are equivalent to 7x - 14 = 21 ?

• x - 2 = 3

• 7x - 20 = 15

• 7x - 14 = 21

Multiple Select

Which equations are equivalent to  $$p-h=24$$  ?

• $$\frac{p-h}{2}=12$$  

• $$\frac{p-h}{3}=6$$  

• $$\frac{p-h}{-4}=-6$$  

• $$\frac{p-h}{-1}=23$$  

​MULTIPLICATION PROPERTY OF EQUALITY

Multiplying both sides of an equal sign by the same number makes an equivalent equation.

is equivalent to

​2x - 9 = 3

and simplifies to

​4(2x - 9) = 3 x 4

​8x - 36 = 12

​Example 3

​If you multiply both sides by 3 what is the result?

​

​8x - 1 = 4

Fill in the Blanks

If both sides are multiplied by 5, what is the result?

$4+7x=-4$  

Multiple Select

Which equations are equivalent to 4 = 6 - 9x?

• $$8=12-18x$$

• $$20=30-45x$$  

• $$12=18-12x$$  

• $$2=4-7x$$  

• $$40=60-9x$$