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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
 

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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
 

 

Equations and Inequalities
Equations: True or False?
Independent Practice
1. Consider the statement: 4 - 3 + 5 = -6 + 8 + 4. This is a mathematically correct sentence.
Is the sentence true or false? Explain how you know.
 
2. Determine if the sentence is true. Select all that apply.
    ⬤   
    ⬤   
    ⬤   
    ⬤   
    ⬤   
 
3. Determine whether the following number sentences are TRUE or FALSE. Justify your answer.
 
                                        
  
 
                                                       
 
 
4. For the equation, x-7=24, can a value be substituted for x to make that a true number sentence? How many values could be substituted for x and have a true number sentence?
 
5. Consider x+4=x+8 . What values could be substituted for x to make this a true number sentence? Explain how you know.
 
6. Determine what value(s) for the variable would make each algebraic equation a true number sentence.
is true for                      _______________.
is true for         _______________.
  is true for         _______________.
 
7. Which of the following has the correct solution given for x? Check all that apply.
 
  ⬤    
  ⬤   
  ⬤    
  ⬤    
  ⬤    
 
 

1. Evaluate the expression 2x - 2 for the value of x = -3

2. Factor: xsquare + 4x - 32 (x-4)(x+8) (x-4)(x-8) (x-4)(x-8) (x-16)

3. Factor: xsquare - 25 (x-5) (x+5)2 (x+5)(x-5) (x-5)(x-5)

4. Evaluate -u2v3 when u=4 and v=-2 128 64 32 -128

5. Using an online calculator, determine whether the value of x=7 is a solution of the equation. x Yes No

6. Explain why x=7 IS or IS NOT a solution of the equation. 7 + 1/x+2=8

7. Solve the equation and check your solution: -2 - 4x = 30

8. Solve the equation and check your solution: 67x - 24 = 3x + 8(8x - 3) 67 -3 -67 All real numbers

9. Solve the equation and check your solution. 5x/2 - x/6 = 14 10 6 7 9

10. Solve the quadratic equation by factoring: xsquare - 6x + 5 = 0 -1, 5 -1,-5 1,-5 1,5

11. The imaginary number i represents:

12. Find real numbers a and b such that the equation is true: a+ bi = 14 + 2i a=16, b=4 a=18, b=6 a=14, b=2 a=15, b=14

13. Find all solutions to the following equation. /4x - 8 = /4x + 9 x = -17/4 x=9 No solution x=-17

14. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for James’ miles.

15. Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz. 10h - .25=450 10h + .25(10h)=450 h -.25 (10h)=450 10h - .25(10h)=450

16. Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work. 17. The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width. Hint: Perimeter = width + length + width + length

18. Twice a number is added to the number and the answer is 80. Write an equation to solve this problem. 2n + n=80 2n = 80 2n + 80=n 80 + n=2n

19. If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20. Multiply the following binomials: (x + 5)(x - 5)

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