Equivalent Equations

Equivalent Equations

(x and /)​

Objective: create and identify equivalent equations.

Fill in the Blanks

WARMUP: ​If 8x - 4 = -9 then 8x - 15 = ?

​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

​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 - 1 = 22

Multiple Select

Which equations are equivalent to p - h = 24?

• $$\frac{p-h}{2}=12$$  

• $$\frac{p-h}{3}=6$$  

• $$\frac{p-h}{-4}=-6$$  

• $$\frac{p-h}{-1}=23$$  

​EXAMPLE

​If 10x - 8 = 22 then 5x - 4 = ?

Fill in the Blanks

​If 35x - 7 = 14 then 5x - 1 = ?

​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

​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 

​EXAMPLE

​Which equations are equivalent to: 3x - 2 = -9

​6x - 2 = -54

​-6x + 4 = 18

​30x - 20 = -90

Multiple Select

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

• 8 = 12 - 18x

• 20 = 30 - 45x

• 12 = 18 - 12x

• -8 = -12 + 18x

• -12 = -18 - 27x

​EXAMPLE

​If 6x + 1 = -3 then 24x + 4 = ?

Fill in the Blanks

​If -3x - 2 = -6 then 6x + 4 = ?