Question

Choose the most appropriate explanation for Line 4. Line 1 4x 2 = 6x Line 2 4x 2 - 6x = 0 Addition Property of Equality Line 3 2x(2x-3) = 0 Distributive Property Line 4 2x = 0 or 2x - 3 = 0 x = 0 or 2x = 3 x =

Answer 1

the answer is zero product property

Answer 2

Zero product property is the most appropriate explanation for Line 4

Explanation:

Given the equation:

`4x^2 = 6x`

Line 1.

`4x^2 = 6x` [Given]

Line 2.

Addition property of equality states that you add same number to both sides of an equation.

Add -6x to both sides we have;

`4x^2-6x =0`

Line 3.

Using the distributive property:

`a \cdot (b+c) = a\cdot b+ a\cdot c`

then;

`2x (2x-3)=0`

Line 4.

Zero product property states that if xy = 0 then either x = 0 or y = 0

by zero product property we have;

2x = 0 or 2x -3

⇒x = 0 or 2x = 3

⇒x = 0 or x = 3/2

Therefore, the most appropriate explanation for Line 4 is, Zero product property