Verify Equation Balance: 26 = x/6 ?= 2/x = 1/78

Are the equations balanced?

$26{=}\frac{x}{6}\stackrel{?}{=}\frac{2}{x}{=}\frac{1}{78}$

To determine whether the given equations are balanced, we begin by examining them step-by-step:

• Given: $26 = \frac{x}{6} \stackrel{?}{=} \frac{2}{x} = \frac{1}{78}$

We should first determine the value of $x$ from the equation involving $\frac{1}{78}$:

• The last equation is $\frac{1}{78} = \frac{2}{x}$.
• Multiplying both sides by $x$ and then by $78$ gives $x = 156$.

Use $x = 156$ to evaluate the other expressions:

• For $\frac{x}{6}$:
• $\frac{156}{6} = 26$

Now, check if all values equate:

• $26 = 26$ from $\frac{x}{6}$
• $26 = 26$ from the right side of the original problem statement

All values match, indicating:

The equations are balanced. Therefore, the correct answer is Yes.