Answer :
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]
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]
