Question

determine which expressions, if any, are equivalent. show your work.
10 ( 4(x - 3) )
( 6x - 2(x - 3) )
( x + 3(x - 2) - 6 )

Explanation:

Step1: Expand \(4(x - 3)\)

Apply distributive property: \(4x - 12\)

Step2: Expand \(6x - 2(x - 3)\)

Distribute \(-2\): \(6x - 2x + 6 = 4x + 6\)

Step3: Expand \(x + 3(x - 2) - 6\)

Distribute \(3\): \(x + 3x - 6 - 6 = 4x - 12\)

Step4: Compare results

\(4(x - 3) = 4x - 12\) and \(x + 3(x - 2) - 6 = 4x - 12\), so they are equivalent. \(6x - 2(x - 3) = 4x + 6\) is different.

Answer:

The equivalent expressions are \(4(x - 3)\) and \(x + 3(x - 2) - 6\).