Questions: Select the simplified form of this expression. 8x-2[20-3(x-4)] After you pick your answer press GO. A. 2x-16 B. 14x+(-16) C. -35x+12 D. 14x+(-64) E. 5x-28

Transcript text: (c) Problem 10: (first taught in lesson 37) Select the simplified form of this expression. \[ 8 x-2[20-3(x-4)] \] After you pick your answer press $G O$. A. $2 x-16$ B. $14 x+(-16)$ C. $-35 x+12$ D. $14 x+(-64)$ E. $5 x-28$

Solution

Simplify the expression $8x - 2[20 - 3(x - 4)]$ and select the correct simplified form from the given options.

Step 1: Simplify the innermost parentheses.

First, simplify $x - 4$. However, since it is already in its simplest form, we proceed to distribute the $-3$ inside the brackets:
\[ -3(x - 4) = -3x + 12 \]

Step 2: Simplify the expression inside the brackets.

Substitute $-3x + 12$ back into the expression:
\[ 20 - 3(x - 4) = 20 - 3x + 12 = 32 - 3x \]

Step 3: Distribute the $-2$ outside the brackets.

Multiply $-2$ by $32 - 3x$:
\[ -2(32 - 3x) = -64 + 6x \]

Step 4: Combine the terms outside the brackets.

Now, combine $8x$ with $-64 + 6x$:
\[ 8x - 64 + 6x = 14x - 64 \]

Step 5: Match the simplified expression with the given options.

The simplified form $14x - 64$ matches option D: $14x + (-64)$.

The simplified form of the expression is $\boxed{14x - 64}$, which corresponds to option D.
The answer is D.

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