Question

(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)

Answer 1

A) Infinite solutions

B) Distributive Property of Multiplication

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.

Answer 2

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.