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)

infinite solutions

Distributive Property

Step-by-step 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

A) all real values of x

B) distributive property

Step-by-step 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

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.