Verified Answer :

  • Identify the linear equation \(3h = 18\).
  • Divide both sides of the equation by \(3\) to isolate the variable \(h\).
  • Simplify the division \(\frac{18}{3}\) to obtain \(h = 6\).
  • The final value is \(\boxed{6}\).

Explanation

  1. Problem Analysis and Initial Approach

The given linear equation is \(3h = 18\). Our goal is to isolate the variable \(h\) and determine its value. To do this, we need to perform an operation that reverses the multiplication of \(h\) by \(3\). Dividing both sides of the equation by the same non-zero number will maintain the equality.

  1. Solving for h

To isolate \(h\), we divide both sides of the equation by \(3\):
\[\frac{3h}{3} = \frac{18}{3}\]
Simplifying the left side, we get \(h\), and calculating the right side, \(18 \div 3 = 6\). Thus, we find that \(h = 6\).

  1. Final Conclusion

We have successfully isolated the variable \(h\) and determined its value to be \(6\). Substituting this back into the original equation, \(3(6) = 18\), confirms that the result is correct. The final value of \(h\) is \(\boxed{6}\).

Examples

Solving for a variable in a linear equation is a fundamental skill in algebra with many real-life applications. For example, if you are planning a group outing and know that the total cost for 3 tickets is \(\$18\), you can use the equation \(3h = 18\) to find the price of a single ticket, where \(h\) represents the cost per person. Solving this gives \(h = \$\frac{18}{3} = \$6\), helping you effectively budget your expenses.

Related Questions