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------------------------------------------------ Mateo is going to solve the equation below. Which of the following represents the equation after combining the like terms?

\[ -8x + 23 - 22x + 9 = 182 \]

A. \[ 14x + 32 = 182 \]

B. \[ -30x + 32 = 182 \]

C. \[ 14x + 14 = 182 \]

D. \[ -30x + 14 = 182 \]

Sure! Let's solve the equation step-by-step to combine the like terms.

We start with the given equation:
[tex]\[ -8x + 23 - 22x + 9 = 182 \][/tex]

1. Combine the [tex]$ x $[/tex]-terms:
The [tex]$ x $[/tex]-terms are [tex]$-8x$[/tex] and [tex]$-22x$[/tex]. When we combine them, we get:
[tex]\[ -8x - 22x = -30x \][/tex]

2. Combine the constant terms:
The constants are [tex]$23$[/tex] and [tex]$9$[/tex]. When we add them together, we get:
[tex]\[ 23 + 9 = 32 \][/tex]

3. Write the simplified equation:
After combining the like terms, the equation becomes:
[tex]\[ -30x + 32 = 182 \][/tex]

Now we have the simplified form of the equation.

Looking at the answer choices:
a. [tex]$ 14x + 32 = 182 $[/tex]
b. [tex]$ -30x + 32 = 182 $[/tex]
c. [tex]$ 14x + 14 = 182 $[/tex]
d. [tex]$ -30x + 14 = 182 $[/tex]

The correct choice is:
[tex]\[ \boxed{-30x + 32 = 182} \][/tex]

So the correct answer is:
b. [tex]$ -30x + 32 = 182 $[/tex]