Equivalent Equations (part 2)

Equivalent Equations

Objective: create and identify equivalent equations.

Multiple Select

Choose all the equivalent expressions.

• 12 + 12 - 3x = 3(x + 8)

• 8 - 3 × 3 + 10 = 50 ÷ 2

• 4x + 12 = 6 + 4x + 6

• 7 - 56 ÷ 7 = -4 + 3

​ADDITION PROPERTY OF EQUALITY

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

​8x + 5 = 13

is equivalent to

8x + 5 + 4 = 13 + 4

8x + 9 = 17

SUBTRACTION PROPERTY OF EQUALITY

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

​8x + 5 = 13

is equivalent to

8x + 5 - 4 = 13 - 4

8x + 1 = 9

​DIVISION PROPERTY OF EQUALITY

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

is equivalent to

​x + 6 = 16

is equivalent to

​2x - 4 = 20

or

​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 - 18 = 25

​EXAMPLE

​Given the equation: 12 = x - y

​

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

​

​

​If you divide both sides by 6 what is the result?

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

​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?

• 20 = 30 - 45x

• 12 = 18 - 27x

• 2 = 3 - 4x

• 40 = 60 - 9x