Question

Latesha justifies whether the expression 4x – 3 is equivalent to One-half (4 x minus 6) minus 2 x (1 minus 3) by letting x = 2 in both expressions. Which values should Latesha compare to justify whether the expressions are equivalent?
2 and 5
5 and 9
5 and 5
9 and 9

Answer 1

To determine whether the expressions \(4x - 3\) and \(\frac{1}{2}(4x - 6) - 2x(1 - 3)\) are equivalent by substituting \(x = 2\), we first need to calculate both expressions for \(x = 2\).

1. **Calculate \(4x - 3\) when \(x = 2\)**:
\[
4(2) - 3 = 8 - 3 = 5
\]

2. **Calculate \(\frac{1}{2}(4x - 6) - 2x(1 - 3)\) when \(x = 2\)**:
- First, calculate \(4(2) - 6\):
\[
4(2) - 6 = 8 - 6 = 2
\]
- Then, compute \(\frac{1}{2}(2)\):
\[
\frac{1}{2}(2) = 1
\]
- Next, calculate \(2(1 - 3)\):
\[
1 - 3 = -2 \quad \text{and thus} \quad 2(-2) = -4
\]
- Finally, combine these results:
\[
1 - 4 = -3
\]

Now, we have:

- For \(4x - 3\), substituting \(x = 2\) yields **5**.
- For \(\frac{1}{2}(4x - 6) - 2x(1 - 3)\), substituting \(x = 2\) yields **-3**.

Since Latesha is comparing the results, she should compare \(5\) (from the first expression) and \(-3\) (from the second expression).

However, it’s also important to note that the option comparisons given are not about -3 but seem to indicate some confusion. The correct values should ideally just denote the outputs without focusing on the options provided.

With regard to the specific given answer options, the correct values to compare are **5 and -3**. Neither of these matches the provided comparison options, which might imply that the options relate to different values.

So, none of the listed comparisons would logically apply to justify whether the expressions are equivalent, since \( 5 \) does not match with any second values provided in the answer options.