Question

1. select all the expressions that are equivalent to $16x - 12 - 24x + 4$. explain or show your reasoning.

$4 + 16x - 12(1 + 2x)$
$40x - 16$
$16x - 24x - 4 + 12$
$-8x - 8$
$10(1.6x - 1.2 - 2.4x + 4)$

Explanation:

Step1: Simplify the original expression

Combine like terms:

$$\begin{align*} 16x - 12 - 24x + 4&=(16x-24x)+(-12+4)\\ &=-8x-8 \end{align*}$$

Step2: Simplify first option

Expand and combine like terms:

$$\begin{align*} 4 + 16x - 12(1 + 2x)&=4+16x-12-24x\\ &=(16x-24x)+(4-12)\\ &=-8x-8 \end{align*}$$

Step3: Simplify second option

No like terms to combine:
$40x - 16$

Step4: Simplify third option

Combine like terms:

$$\begin{align*} 16x - 24x - 4 + 12&=(16x-24x)+(-4+12)\\ &=-8x+8 \end{align*}$$

Step5: Simplify fourth option

No like terms to combine:
$-8x - 8$

Step6: Simplify fifth option

Expand and combine like terms:

$$\begin{align*} 10(1.6x - 1.2 - 2.4x + 4)&=16x-12-24x+40\\ &=(16x-24x)+(-12+40)\\ &=-8x+28 \end{align*}$$

Answer:

The equivalent expressions are:

1. $4 + 16x - 12(1 + 2x)$
2. $-8x - 8$