Question

which equation is equivalent to \\(-k + 0.03 + 1.01k = -2.45 - 1.81k\\)?

\\(\bigcirc\\) \\(-100k + 3 + 101k = -245 - 181k\\)
\\(\bigcirc\\) \\(-100k + 300 + 101k = -245 - 181k\\)
\\(\bigcirc\\) \\(-k + 3 + 101k = -245 - 181k\\)
\\(\bigcirc\\) \\(-k + 300 + 101k = -245 - 181k\\)

Explanation:

Identify the given equation and goal

The given equation is:

$$-k + 0.03 + 1.01k = -2.45 - 1.81k$$

We want to find an equivalent equation from the given multiple-choice options. Looking at the options, all decimal coefficients have been converted to integers, suggesting we need to clear the decimals.

Apply multiplication to clear decimals

Using the Linear Equation Solving knowledge point

$$
LATEXBLOCK0
$$

Match with the given options

We compare our resulting equation with the choices:

1. \(-100k + 3 + 101k = -245 - 181k\) (Matches our result)
2. \(-100k + 300 + 101k = -245 - 181k\)
3. \(-k + 3 + 101k = -245 - 181k\)
4. \(-k + 300 + 101k = -245 - 181k\)

Answer:

• (A) \(-100k + 3 + 101k = -245 - 181k\) (Correct answer)
• (B) \(-100k + 300 + 101k = -245 - 181k\)
• (C) \(-k + 3 + 101k = -245 - 181k\)
• (D) \(-k + 300 + 101k = -245 - 181k\)