Select all of the equations below that are equivalent to: $\newline$ $18 - c = 15$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $18 - c - 10 = 6$ $\newline$ (B) $18 - c - 12 = 3$ $\newline$ (C) $18 - c - 2 = 13$ $\newline$ (D) $18 - c - 12 = 5$

Full solution

Q. Select all of the equations below that are equivalent to:

\newline

18 - c = 15

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

18 - c - 10 = 6

\newline

(B)

18 - c - 12 = 3

\newline

(C)

18 - c - 2 = 13

\newline

(D)

18 - c - 12 = 5

Original Equation: We start with the original equation: $18 - c = 15$ . To find equivalent equations, we can add or subtract the same value from both sides of the equation. Let's check each option by applying the properties of equality.
Option (A) Analysis: For option (A), we subtract $10$ from both sides of the original equation: $(18 - c) - 10 = 15 - 10$ . Calculating the right side, we get $15 - 10 = 5$ . So, the equation becomes $18 - c - 10 = 5$ , which is not the same as option (A), which states $18 - c - 10 = 6$ .
Option (B) Analysis: For option (B), we subtract $12$ from both sides of the original equation: $(18 - c) - 12 = 15 - 12$ . Calculating the right side, we get $15 - 12 = 3$ . So, the equation becomes $18 - c - 12 = 3$ , which matches option (B).
Option (C) Analysis: For option (C), we subtract $2$ from both sides of the original equation: $(18 - c) - 2 = 15 - 2$ . Calculating the right side, we get $15 - 2 = 13$ . So, the equation becomes $18 - c - 2 = 13$ , which matches option (C).
Option (D) Analysis: For option (D), we subtract $12$ from both sides of the original equation: $(18 - c) - 12 = 15 - 12$ . Calculating the right side, we get $15 - 12 = 3$ . So, the equation becomes $18 - c - 12 = 3$ , which is not the same as option (D), which states $18 - c - 12 = 5$ .