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

Question

Are the equations balanced?

26=x6=?2x=178 26{=}\frac{x}{6}\stackrel{?}{=}\frac{2}{x}{=}\frac{1}{78}

Video Solution

Step-by-Step Solution

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

  • Given: 26=x6=?2x=17826 = \frac{x}{6} \stackrel{?}{=} \frac{2}{x} = \frac{1}{78}

We should first determine the value of xx from the equation involving 178\frac{1}{78}:

  • The last equation is 178=2x\frac{1}{78} = \frac{2}{x}.
  • Multiplying both sides by xx and then by 7878 gives x=156x = 156.

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

  • For x6\frac{x}{6}:
  • 1566=26\frac{156}{6} = 26

Now, check if all values equate:

  • 26=2626 = 26 from x6\frac{x}{6}
  • 26=2626 = 26 from the right side of the original problem statement

All values match, indicating:

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

Answer

Yes