Pregunta
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\( x = \frac{1}{2} \)
Solución
To solve the equation \( 8x + 2 + 3x + 5 = x + 12 \) for \( x \), follow these steps:
1. **Combine like terms on the left side:**
\[
8x + 3x + 2 + 5 = x + 12
\]
\[
11x + 7 = x + 12
\]
2. **Move all terms containing \( x \) to one side and constant terms to the other:**
\[
11x - x = 12 - 7
\]
\[
10x = 5
\]
3. **Solve for \( x \) by dividing both sides by 10:**
\[
x = \frac{5}{10}
\]
\[
x = \frac{1}{2}
\]
**Final Answer:**
\[
x = \frac{1}{2}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
To solve for \( x \) in the equation \( 8x + 2 + 3x + 5 = x + 12 \), first, combine like terms on the left side: 1. Combine the \( x \) terms: \( 8x + 3x = 11x \). 2. Combine the constant terms: \( 2 + 5 = 7 \). So, the equation simplifies to: \[ 11x + 7 = x + 12 \] Next, isolate \( x \) by subtracting \( x \) from both sides: \[ 11x - x + 7 = 12 \] \[ 10x + 7 = 12 \] Now, subtract 7 from both sides: \[ 10x = 12 - 7 \] \[ 10x = 5 \] Finally, divide both sides by 10 to solve for \( x \): \[ x = \frac{5}{10} = \frac{1}{2} \] So, the solution is: \[ x = \frac{1}{2} \]
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