Question:

Consider the following sequence of steps to solve the equation: - 15 + 4x + 4x2 = 0

Step 1 ⇒ 4x2 + 4x - 15 = 0

Step 2 ⇒ 4x2 - 6x + 10x - 15 = 0

Step 3 ⇒ 2x (2x - 3) + 5 (2x - 3) = 0

Step 4 ⇒ (2x + 5) (2x - 3) = 0

Step 5 ⇒ x = - 3/2 or x = 5/2

A. Explain why Step 1 is valid using properties of the real number system.

Show possible intermediate steps to support your explanation.

A. Explain why Step 4 is valid.

Question

Tucker Snyder

Mathematics

2 August, 13:36

Question:

Consider the following sequence of steps to solve the equation: - 15 + 4x + 4x2 = 0

Step 1 ⇒ 4x2 + 4x - 15 = 0

Step 2 ⇒ 4x2 - 6x + 10x - 15 = 0

Step 3 ⇒ 2x (2x - 3) + 5 (2x - 3) = 0

Step 4 ⇒ (2x + 5) (2x - 3) = 0

Step 5 ⇒ x = - 3/2 or x = 5/2

A. Explain why Step 1 is valid using properties of the real number system.

Show possible intermediate steps to support your explanation.

A. Explain why Step 4 is valid.

+1

Answers (1)

Know the Answer?

Hannah Phillips · Answer 1

Step 1:

Addition is commutative

A + B = B + A

So the terms can be rearranged

Step 4:

2x (2x - 3) + 5 (2x - 3)

Since (2x - 3) is common to both terms,

You can take it common

(2x - 3) (2x + 5)

This can be proved verified using distribution property

(2x - 3) (2x + 5) is the same as

(2x + 5) (2x - 3) because multiplication is commutative