(07.05 MC) An equation is shown below: 8x + 2(x – 7) = 7x + 3x – 14 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points)

Step by step:

8x + 2(x-7) = 7x + 3x - 14

1. distribute the 2 to the parenthese (x-7)

8x + 2x - 14 = 7x + 3x - 14

2. combine like terms

8x + 2x = 10x

7x + 3x = 10x

10x - 14 = 10x - 14

3. get your variables to one side by adding 14 to both sides

10x - 14 = 10x - 14

     + 14          +14

10x = 10x

4. solve for variable x by dividing both sides by 10

10x = 10x

/10      /10

x = x

Answers:

Becuase x=x, it can equal any value meaning there are infinite solutions.

One property used is the addition property of equality when adding 14 to both sides of the equation.

A) Infinite solutions

B) Distributive Property of Multiplication

Step-by-step explanation:

=> 8x+2(x-7) = 7x+3x-14

(Using distributive Property to expand brackets)

=> 8x+2x-14 = 10x-14

=> 10x-14 = 10x -14

(Subtracting 10x to both sides)

=> 10x-10x-14 = -14

=> -14 = -14

So, This equation has infinite solutions.

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