Question

PLEASE HELP 100 PTS!

4.
(07.05 MC)

An equation is shown below:

5x + 3(x − 5) = 6x + 2x − 15

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) all real values of x

B) distributive property

Explanation:

A)

5x + 3(x − 5) = 6x + 2x − 15

5x + 3x - 15 = 8x - 15

8x - 15 = 8x - 15

-15 = -15

This is an identity, true for all real values of x

Answer 2

infinite solutions

Distributive Property

Explanation:

5x + 3(x − 5) = 6x + 2x − 15

Distribute

5x+3x -15 = 6x+2x -15

Combine like terms

8x -15 = 8x-15

Subtract 8x from each side

8x-8x-15 = 8x-8x-15

-15=-15

This is always true so there are infinite solutions

We used the Distributive Property

And the Subtraction Property of Equality