Foundations of Algebra Solving Equations

How many solutions does the equation have? 

2(4 + 3x) = (9x − 2) − (x + 4)

• 1 solution

• 2 solutions

• Infinitely many solutions

• no solutions

Using the appropriate property of equality, which one of the following is a valid next step for solving the equation 7x + 20 = 4 − x ? 

• 7x + 24 = −x 

  
  

• 8x + 20 = 4

• 7x = 24 − x

• 20 = 4 + 6x 

  
  

Which equation is equivalent to 

7(b − 4) = 5(b + 4) + 6? 

• 
  7b − 4 = 5b + 10

• 7b − 4 = 5b + 24

• 7b − 28 = 5b + 26

• 7b− 28 = 5b + 50

Select the box that correctly identifies the only solution or the best description of how many solutions there are for each equation.

Write the number for the choice you select.

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Steven needs to solve the equation 6x + 10 = 2(x - 5).

Which equations represent a first step Steven could use to solve the original equation?

Select all that apply. 

• Steven subtracts 2 from both sides of the equation to get 6x + 8 = x - 5. 

• Steven subtracts 10 from both sides of the equation to get 6x = 2(x - 15). 

• Steven distributes 2 on the right side of the equation to get 6x + 10 = 2x - 10.

• Steven divides both sides of the equation by 10 to get 6x + 1 = 5(x - 5). 

• Steven divides both sides of the equation by 2 to get 3x + 5 = x - 5.

Harper has an amount of money saved that can be represented by the expression 4x + 16.

Her friend Margaret has savings represented by the expression 8x + 32.

Which describes how Margaret's amount of money saved compares to Harper's amount saved? 

• Margaret's amount saved is 2 times as much as Harper's amount saved. 

• Margaret's amount saved is 4 times as much as Harper's amount saved. 

• Margaret's amount saved is 6 times as much as Harper's amount saved.

• Margaret's amount saved is 8 times as much as Harper's amount saved.

The formula for the perimeter (P) of a rectangle is P = 2L + 2W. 

What should be the first step when 

solving for W? 

• P + 2L = 2W 

• P − 2L = 2W 

• P + 2W = 2L 

• P − 2W = 2L

If 2x − 9 = 15 − x, then x =

• 2

• 4

• 6

• 8

Bronson earns an amount of money that can be represented by the expression 12x + 6. His friend Robbie's earnings can be represented by the expression 48x + 24.

Which describes how Bronson's amount of money earned compares to Robbie's amount earned?

• Bronson's amount earned is 2 times as much as Robbie's amount earned.
  

• Bronson's amount earned is 4 times as much as Robbie's amount earned.

• Bronson's amount earned is 1/2 as much as Robbie's amount earned.

• Bronson's amount earned is 1/4 as much as Robbie's amount earned. 

Please solve this equation

1.2x = 9.6

• x = 8

• x = 10.8

• x = 8.4

• None of these match my answer