Select the correct answer. Which algebraic expression is equivalent to the expression below? $$ \begin{array}{ll}3(5 x+7)-6(4-2 x) \ \begin{array}{ll}\text { O } & 12 x+27 \ \text { O } & 12 x+3\end{array} \ \begin{array}{ll}-12\end{array} \ 27 x-12\end{array} $$

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Subtract the terms:
  $$3\left(5x+7\right)-6\left(4-2x\right)$$
- step1: Expand the expression:
  $$15x+21-6\left(4-2x\right)$$
- step2: Expand the expression:
  $$15x+21-24+12x$$
- step3: Add the terms:
  $$27x-3$$
To simplify the expression $$ 3(5x + 7) - 6(4 - 2x) $$, we can follow these steps:

1. **Distribute the terms**:
   - For $$ 3(5x + 7) $$:
     $$
     3 \cdot 5x + 3 \cdot 7 = 15x + 21
     $$
   - For $$ -6(4 - 2x) $$:
     $$
     -6 \cdot 4 + (-6) \cdot (-2x) = -24 + 12x
     $$

2. **Combine the results**:
   $$
   15x + 21 - 24 + 12x
   $$

3. **Combine like terms**:
   - Combine $$ 15x $$ and $$ 12x $$:
     $$
     15x + 12x = 27x
     $$
   - Combine $$ 21 $$ and $$ -24 $$:
     $$
     21 - 24 = -3
     $$

Thus, the simplified expression is:
$$
27x - 3
$$

Now, comparing this with the provided options:
- $$ 12x + 27 $$
- $$ 12x + 3 $$
- $$ -12 $$
- $$ 27x - 12 $$

None of the options match $$ 27x - 3 $$. Therefore, it seems there might be an error in the options provided. The correct equivalent expression is $$ 27x - 3 $$.
The correct equivalent expression is $$ 27x - 3 $$.

Select the correct answer. Which algebraic expression is equivalent to the expression below? \[ \begin{array}{ll}3(5 x+7)-6(4-2 x) \\ \begin{array}{ll}\text { O } & 12 x+27 \\ \text { O } & 12 x+3\end{array} \\ \begin{array}{ll}-12\end{array} \\ 27 x-12\end{array} \]

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions