Question
Solve. \[ 2(3 x+12)=2(4 x+8) \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{ \}. (Simplify your answer.) B. The solution set is \{all real numbers\}. C. The solution set is \( \varnothing \).
Ask by Hampton Martinez. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \(\{4\}\).
Solution
We start with the equation
\[
2(3x+12)=2(4x+8).
\]
First, divide both sides by 2:
\[
3x+12=4x+8.
\]
Next, subtract \(3x\) from both sides:
\[
12=x+8.
\]
Then, subtract 8 from both sides:
\[
x=4.
\]
Thus, the solution set is \(\{4\}\).
Since none of the provided choices exactly state \(\{4\}\), the correct selection is to complete choice A with the answer \(\{4\}\).
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Simplify this solution Bonus Knowledge
Let's solve the equation step-by-step: Starting with: \[ 2(3x + 12) = 2(4x + 8) \] 1. Distribute the 2 on both sides: \[ 6x + 24 = 8x + 16 \] 2. Rearrange the equation by moving all terms involving \( x \) to one side and constant terms to the other side: \[ 6x - 8x = 16 - 24 \] This results in: \[ -2x = -8 \] 3. Now, divide both sides by -2: \[ x = 4 \] The solution set is \( \{4\} \). Thus, the correct choice is: A. The solution set is \{4\}.
