To determine which expressions are equivalent to \(-6(3x - 7)\), we first simplify that expression:
\[ -6(3x - 7) = -6 \cdot 3x + 6 \cdot 7 = -18x + 42. \]
Now we will simplify each expression in the table to see which ones are equivalent to \(-18x + 42\).
-
\(-18x - 7\): \[ -18x - 7 \quad (\text{Not equivalent because it lacks the } +42) \]
-
\(4 - 10(3x - 7)\): \[ 4 - 10(3x - 7) = 4 - 30x + 70 = -30x + 74 \quad (\text{Not equivalent}) \]
-
\(4(3x + 5) - 2(15x - 11)\): \[ 4(3x + 5) - 2(15x - 11) = (12x + 20) - (30x - 22) = 12x + 20 - 30x + 22 = -18x + 42 \quad (\text{Equivalent}) \]
-
\(6(3x + 7)\): \[ 6(3x + 7) = 18x + 42 \quad (\text{Not equivalent}) \]
-
\(2x - 7 - 5(4x - 7)\): \[ 2x - 7 - 5(4x - 7) = 2x - 7 - 20x + 35 = -18x + 28 \quad (\text{Not equivalent}) \]
-
\(-2(9x - 21)\): \[ -2(9x - 21) = -18x + 42 \quad (\text{Equivalent}) \]
Now, compiling the results, the expressions that are equivalent to \(-6(3x - 7)\) are:
- \(4(3x + 5) - 2(15x - 11)\)
- \(-2(9x - 21)\)
Thus, the equivalent expressions are:
- \(4(3x + 5) - 2(15x - 11)\)
- \(-2(9x - 21)\)