Finding Equivalent Equations

Equivalent Equations

Objective: create and identify equivalent equations.

​Vocabulary

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

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​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

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​

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​2(x + 9) = 24 + 2x - 15

​?

​?

​EXAMPLE

Multiple Select

Choose all the equivalent expressions.

• 56 ÷ 7 = 4 + 3

• 3x + 12 = 6 + 3x + 6

• 4(x - 5) = 3x - 20 + x

• 6 + 2 x 4 - 7 = 30 - 5

​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

​EXAMPLE

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

​

​3x - 15 = 32

Multiple Choice

What is the equation after you ADD 3 to both sides and simplify it?

3x - 5 = -2

• 3x - 8 = -5

• 6x - 8 = -5

• 3x - 2 = 1

• 6x - 1 = 1

• 3x - 1 = -5

Fill in the Blanks

What is the equation after you ADD 12 to both sides and simplify it?

2x - 8 = -1

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

Multiple Choice

What is the equation after you SUBTRACT 4 from both sides and simplify it?

9x + 8 = -4

• 5x - 4 = 0

• 5x - 4 = -8

• 9x - 4 = 0

• 9x + 4 = -8

Fill in the Blanks

What is the equation after you SUBTRACT 5 from both sides and simplify it?

4x + 12 = 24