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.

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

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day

answer:  

step-by-step explanation:

odd numbers are only divisible by 1 and itself.

even numbers are divisible by more than 1 and itself.

for example 6 is even because it is divisible by more than 1 and its self. 1 x 6= 6 ; 2 x 3= 6

and 7 is odd because only 7 x 1 equals seveb