Question
Solve the equation by dividing both sides: \( 2(x+12)=4 x-6 \)
Ask by Ellis Donnelly. in Egypt
Jan 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 15 \)
Solution
Sure, let's solve the equation step by step by dividing both sides as needed.
**Given Equation:**
\[
2(x + 12) = 4x - 6
\]
**Step 1: Distribute the 2 on the left side**
\[
2 \cdot x + 2 \cdot 12 = 4x - 6
\]
\[
2x + 24 = 4x - 6
\]
**Step 2: Move all terms containing \( x \) to one side and constants to the other**
Subtract \( 2x \) from both sides:
\[
2x + 24 - 2x = 4x - 6 - 2x
\]
\[
24 = 2x - 6
\]
**Step 3: Isolate the term with \( x \)**
Add \( 6 \) to both sides:
\[
24 + 6 = 2x - 6 + 6
\]
\[
30 = 2x
\]
**Step 4: Solve for \( x \) by dividing both sides by 2**
\[
\frac{30}{2} = \frac{2x}{2}
\]
\[
15 = x
\]
**Solution:**
\[
x = 15
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To solve the equation \( 2(x+12)=4x-6 \), we start by dividing both sides by 2 for simplicity. This gives us: \( x + 12 = 2x - 3 \). Now, let's move \( x \) to one side by subtracting \( x \) from both sides: \( 12 = x - 3 \). Next, add 3 to both sides: \( 15 = x \). So the solution is \( x = 15 \).
