Question

solving equations with the distributive property - item 2452
which sentence explains the correct first step in the solution of this equation?
$4(x - 3) = 9$
add 2 to both sides.
apply the distributive property to get $4x - 12 = 9$.
apply the distributive property to get $4x - 3 = 9$.
subtract 9 from both sides.

Explanation:

To solve the equation \(4(x - 3)=9\), the distributive property ( \(a(b - c)=ab - ac\) ) is used first. Applying it to \(4(x - 3)\), we multiply 4 by \(x\) and 4 by \(-3\), resulting in \(4x-12 = 9\). The other options are incorrect: adding 2 or subtracting 9 are not the first step here, and the third option misapplies the distributive property (it should be \(-12\), not \(-3\)).

Answer:

The option: "Apply the distributive property to get \(4x - 12 = 9\)." (the one with this text among the choices)