Question

When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
Original Equation:
Original Equation:
one sixth, left parenthesis, minus, 12, x, squared, right parenthesis, plus, 4, equals, minus, x, squared, minus, 2
6
1
​
(−12x
2
)+4=
−x
2
−2
First Step:
First Step:
minus, 2, x, squared, plus, 4, equals, minus, x, squared, minus, 2
−2x
2
+4=
−x
2
−2

Answer 1

To understand Drew's first step in solving the equation \(\frac{1}{6} (-12x^2) + 4 = -x^2 - 2\), let's analyze the transformation that took place.

The original left-hand side has the expression \(\frac{1}{6} (-12x^2)\). When Drew simplified this, he multiplied \(-12x^2\) by \(\frac{1}{6}\):

\[
\frac{1}{6} \cdot (-12x^2) = -2x^2
\]

Thus, the original equation simplifies to:

\[
-2x^2 + 4 = -x^2 - 2
\]

The property that justifies this step is the **Multiplicative Property of Equality**, which states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. In this case, Drew is effectively applying the concept that \(\frac{1}{6} \cdot (-12) = -2\).

Hence, the correct justification for Drew's first step is the **Multiplicative Property of Equality**.