Question
Solve the equation.
12 left parenthesis x plus 3 right parenthesis equals 3 left parenthesis 4 x plus 2 right parenthesis plus 30
Question content area bottom
Part 1
A.36
36
B.
All real numbers
C.
No solution
D.
0
12 left parenthesis x plus 3 right parenthesis equals 3 left parenthesis 4 x plus 2 right parenthesis plus 30
Question content area bottom
Part 1
A.36
36
B.
All real numbers
C.
No solution
D.
0
Answers
Answered by
GPT-4o mini
To solve the equation \( 12(x + 3) = 3(4x + 2) + 30 \), let's first simplify both sides.
1. Distribute on both sides:
\[
12x + 36 = 12x + 6 + 30
\]
2. Combine like terms on the right side:
\[
12x + 36 = 12x + 36
\]
Now, if we subtract \( 12x \) from both sides:
\[
36 = 36
\]
Since this is a true statement, it means that the equation holds for all values of \( x \). Therefore, the solution to the equation is:
**B. All real numbers**.
1. Distribute on both sides:
\[
12x + 36 = 12x + 6 + 30
\]
2. Combine like terms on the right side:
\[
12x + 36 = 12x + 36
\]
Now, if we subtract \( 12x \) from both sides:
\[
36 = 36
\]
Since this is a true statement, it means that the equation holds for all values of \( x \). Therefore, the solution to the equation is:
**B. All real numbers**.
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