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Algebra
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Solve each equation and explain each step of your process using properties of equality, inverse, and identity

 

4/x = 1/x + x^2 + 4x - 12 / x^2

 

1/3x^2 = 1/6 + 1/6x

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Related questions

Equations and Inequalities
Identifying Properties When Solving Equations
Independent Practice
 
1. The following pairs of equations are equivalent. Describe the operation that occurred in the second equation.
 
 
 
 
 
 
2. Complete the following table with the properties used to solve 4(x+3)=20.
 
Statement Proof
4 (x+3) = 20 Given
4x + 12 = 20  
4x = 8  
x = 2  

3. Complete the following table with the mathematical statements that correspond to the proofs used to solve  

Statement Proof
  Given
  Multiplication Property of Equality
  Distributive Property
  Addition Property of Equality
  Division Property of Equality
 
4. Consider the equations 5x + 10 = 30 and 5 (x+10) = 30.
Do they have the same solution? Why or why not?
 
5. Consider the equations 3x + 2 = 14 and 2+3x = 14.
Do they have the same solution? Why or why not?
 
6. Consider the equation 3 (x+2)+3x = 36
Without solving. Name all the properties that would be used to solve the equation.
 
7. Consider the equation  
Part A: Write an equivalent equation using the multiplication property of equality.
Part B: What properties will you use next to solve the equation?
8. Solve the following equation. Justify each step.
0.2x + 3.1 - 2.1x = 0.3 (x-5) + 0.2
 

 

7. Consider the equation  
 
Part A: Write an equivalent equation using the multiplication property of equality.
Part B: What properties will you use next to solve the equation?
 
8. Solve the following equation. Justify each step.
0.2x + 3.1 - 2.1 x = 0.3 (x-5) + 0.2
 

Explain in your own words how to solve a linear equation using the equality properties. Give an example.

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