Equivalent Equations

Equivalent Equations

(+ and -)​

Objective: create and identify equivalent equations.

​Vocabulary

Equivalent: 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

Are the following expressions equivalent?

​4 + 2 x 3 - 2 = 44 ÷ 2​

​?

​?

​EXAMPLES

​2(x + 9) = 24 + 2x - 6

Multiple Select

Choose all the equivalent expressions.

• $$12+12-3x=3(x+8)$$  

• $$8-3\times3+5=10-12\div2$$  

• $$4x+12=4x+6+6$$  

• $$56\div7=4+3$$  

​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

​EXAMPLE

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

​

​3x - 15 = 32

Fill in the Blanks

If 4 is added to both sides, you simplify both sides, what is the resulting equation?

5x + 9 = 3

Fill in the Blanks

If 9 is added to both sides, you simplify both sides, what is the resulting equation?

2x - 3 = 8

​EXAMPLE

​Which equations are equivalent to: 4x - 1 = 6

​4x + 6 = 12

​4x + 2 = 9

​4x - 2 = 7

Multiple Select

Which equation(s) are equivalent to 3x - 10 = 6 ?

• 3x - 6 = 10

• 3x - 15 = 11

• 3x = 16

​EXAMPLE

​If 4x - 1 = 6 then 4x + 5 = ?

Fill in the Blanks

​If -7x - 6 = 13 then -7x - 5 = ?

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 6 is subtracted from both sides what is the result?

​

​7x - 22 = 10

Fill in the Blanks

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

12x + 9 = 15

Fill in the Blanks

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

4x - 12 = -24

​EXAMPLE

​Which equations are equivalent to: 8x - 3 = 4

​8x - 6 = 1

​8x - 2 = 3

​8x - 4 = 3

Multiple Select

Which equation(s) are equivalent to 9x + 7 = -11 ?

• 9x + 3 = -15

• 9x + 3 = -7

• 9x + 11 = -15

​EXAMPLE

​If 3x + 9 = -7 then 3x + 2 = ?

Fill in the Blanks

​If 8x + 2 = -5 then 8x - 5 = ?