Question

proving equivalent expressions
use properties to prove that the expressions are equivalent. complete the statements.
prove ( 7x - 4x = 3x ).
use the distributive property to factor out the ( x ), and the expression becomes (langle
angle).
complete the subtraction inside the parentheses, and the expression becomes (langle
angle).
use the commutative property of multiplication, and the expression becomes (langle
angle).

Explanation:

Step1: Apply Distributive Property

The distributive property states that \(a(b + c)=ab + ac\), and in reverse, \(ab - ac=a(b - c)\). For \(7x-4x\), we factor out \(x\):
\(7x - 4x=x(7 - 4)\)

Step2: Subtract Inside Parentheses

Calculate \(7 - 4\) inside the parentheses:
\(x(7 - 4)=x(3)\)

Step3: Apply Commutative Property of Multiplication

The commutative property of multiplication states that \(a\times b = b\times a\). So \(x(3)=3x\).

Answer:

To prove \(7x - 4x = 3x\):

1. Distributive Property: \(7x - 4x=x(7 - 4)\)
2. Subtraction: \(x(7 - 4)=x(3)\)
3. Commutative Property: \(x(3)=3x\)

Thus, \(7x - 4x = 3x\) is proven.