Question

An expression is shown.

6-2 (4x – 7)
Which of the following expressions are equivalent to the given expression? Select all that apply.

A. -8 (x+1)
B. -8x + 20
C. 4 (4x – 7)
D. -4 (2.-5)

Answer 1

After simplifying the given expression, 6 - 2(4x - 7), the only equivalent expression from the choices provided is option B: -8x + 20.

Step-by-step explanation:

The student is asking which expressions are equivalent to the given expression 6 - 2(4x - 7). First, let's simplify the given expression by distributing the -2 across the terms inside the parentheses.

6 - 2(4x - 7) = 6 - 8x + 14 = 20 - 8x

Now, let's compare the simplified expression to the choices provided:

• A. -8(x+1) would simplify to -8x - 8, which is not equivalent.
• B. -8x + 20 is the same as the simplified expression we found, so it is equivalent.
• C. 4(4x - 7) would simplify to 16x - 28, which is not equivalent.
• D. -4(2 - 5) simplifies to -4(-3), which is 12. This does not look like the simplified expression of the original, so it is not equivalent.

Therefore, only option B is equivalent to the given expression 6 - 2(4x - 7).