Equivalent Equations Justify your reasoning. Image from

Equivalent EquationsJustify your reasoning.

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Learning Goal for Focus 2 (HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3):The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step.

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In addition to level 3.0 and above and beyond what was taught in class, the student may:- Make connection with other concepts in math- Make connection with other content areas.

The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step. - rearrange formulas to highlight a quantity of interest.-Graph created equations on a coordinate graph.

The student will be able to solve linear equations and inequalities in one variable and explain the logic in each step.- Use

equations and inequalities in one variable to solve problems.

With help from theteacher, the student haspartial success with solving linear equations and inequalities in one variable.

Even with help, the student has no success with solving linear equations and inequalities in one variable.

Write an equation that is true when…

1. x = 0

2. t = 1 or -1

3. y = -0.5

4. z = π

Examples:1. 3x = 0

2. 5t – 4 = 1

3. -32y - 24 = -8

4. z(52) = 25π


Why would each of the following equations have the SAME solution set?

3x = 1 + x and 3x = x + 1The commutative property.

3x = (1 + x) + 5 and 3x = 1 + (x + 5)The associative property.

(A solution set is the group of all answers to an equation.)


Would each of the following equations have the same solution set? Why or why not?

3x = 1 + x and 3x + 500 = 1 + x + 500Yes. The subtraction property of equality could subtract 500 from both sides of the 2nd equation. Then they would be equivalent.

3x = 1 + x and 9x = 3(x + 1)Yes. The division property of equality could divide 3 from both sides of the 2nd equation. Then they would be equivalent.


Write an equation that would be equivalent to…

• -6x - 4 = x – 9

• What algebraic property did you use?

• Share your equation with a neighbor to verify that it is equivalent.

• 16x – 8 = 4x

• What algebraic property did you use?

• Share your equation with a neighbor to verify that it is equivalent.


The equation 2x + 4 = 6x – 2 is equivalent to all of the following. Which property was used to change the equation?

1. -2x – 4 = -6x + 2

2. 4 = 4x – 2

3. 2x + 2 = 6x – 4

4. 3x + 4 = 7x – 2

5. x + 2 = 3x – 1

6. 2x – 1 = 6x - 7

1. Multiplication property (•-1)

2. Subtraction property (-2x)

3. Subtraction property (-2)

4. Addition property (+x)

5. Division property (÷2)

6. Subtraction property (-5)

Match up equations with the same solution. Explain how you know they had the same solution using properties.

A. 2x – 3 = 5x + 7B. 2x + 3 = 5x – 7C. 10x – 8 = 6x + 10D. 2x – 2 = 5x – 12E. 4x – 6 = 10x + 14F. 5x – 4 = 3x + 5

• A & E = Multiplication property (•2)• B & D = Subtraction

property (-5)• C & F = Division property

(÷2)


Equivalent Equations Justify your reasoning. Image from

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