Final answer:
The expressions equivalent to -6(3x - 7) are 4(3x + 5) - 2(15x - 11) and -2(9x - 21), as both simplify to -18x + 42, which is the expanded form of the original expression.
Step-by-step explanation:
To determine which expressions are equivalent to -6(3x - 7), we need to simplify or expand the given expressions and check if they result in the same expression as -6(3x - 7).
- Let's first simplify the original expression:
-6 × 3x = -18x
-6 × -7 = +42
So, the simplified form is -18x + 42. - Looking at the given options:
- -18x - 7 is not equivalent because it does not include the +42 term.
- 4 - 10(3x - 7) simplifies to -30x + 70 + 4, which is not equivalent.
- 4(3x + 5) - 2(15x - 11) simplifies to 12x + 20 - 30x + 22, which simplifies further to -18x + 42, so this expression is equivalent.
- 6(3x + 7) simplifies to 18x + 42, which is not equivalent because it has a positive coefficient for x.
- 2x - 7 - 5(4x - 7) simplifies to 2x - 7 - 20x + 35, which further simplifies to -18x + 28, and is not equivalent.
- -2(9x - 21) simplifies to -18x + 42, which is equivalent.
Therefore, the expressions equivalent to -6(3x - 7) are 4(3x + 5) - 2(15x - 11) and -2(9x - 21).