Pregunta
Solve the following equation. \[ 6-\frac{x}{7}=2+\frac{x}{7} \]
Ask by Kelly Harper. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( x = 14 \)
Solución
To solve the equation:
\[
6 - \frac{x}{7} = 2 + \frac{x}{7}
\]
**Step 1:** Move all terms involving \( x \) to one side and the constant terms to the other side.
Subtract \( \frac{x}{7} \) from both sides:
\[
6 = 2 + \frac{2x}{7}
\]
**Step 2:** Subtract 2 from both sides to isolate the term with \( x \):
\[
4 = \frac{2x}{7}
\]
**Step 3:** Solve for \( x \) by multiplying both sides by 7:
\[
28 = 2x
\]
**Step 4:** Divide both sides by 2:
\[
x = 14
\]
**Answer:** \( x = 14 \)
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Simplifique esta solución Extra Insights
To solve the equation \( 6 - \frac{x}{7} = 2 + \frac{x}{7} \), we start by isolating \( x \). First, let’s eliminate the fractions by multiplying both sides of the equation by \( 7 \) to make it easier to work with: \[ 7 \left(6 - \frac{x}{7}\right) = 7\left(2 + \frac{x}{7}\right) \] This simplifies to: \[ 42 - x = 14 + x \] Next, we want to isolate \( x \). Begin by adding \( x \) to both sides: \[ 42 = 14 + 2x \] Then, subtract \( 14 \) from both sides: \[ 28 = 2x \] Now, divide both sides by \( 2 \) to solve for \( x \): \[ x = 14 \] Thus, the solution to the equation is: \[ \boxed{14} \]
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